Questions on Geometry: Parallelograms answered by real tutors!

Algebra ->  Algebra  -> Parallelograms -> Questions on Geometry: Parallelograms answered by real tutors!      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Tutors Answer Your Questions about Parallelograms (FREE)

Question 571674: 2+2
Answer by Alan3354(21580) About Me  (Show Source):
Question 571359: Hello there! This is a question I had on a test review worksheet, that i didn't quite understand.
"Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, which statement must be true?"
A: Quadrilateral ABCD is a square
B: Quadrilateral ABCD is a rhombus
C: Quadrilateral ABCD is a rectangle
D: Quadrilateral ABCD is an isosceles trapezoid
I have eliminated "B" and "D", but I am unsure as to whether ABCD is square or rectangle. Could you kindly explain as to why it is either one?
Found 2 solutions by solver91311, Alan3354:
Answer by solver91311(12121) About Me  (Show Source):
You can put this solution on YOUR website!


The key phrase in the question is "must be"

You don't know anything about the relative measures of the adjacent sides, so while the figure certainly could be a square, or a rhombus for that matter since a square is just a special case of the rhombus, the congruence of adjacent angles demands that the quadrilateral be at least a rectangle.

In fact, your quadrilateral could be a trapezoid because there is some disagreement on the allowed number of parallel sides in a trapezoid. At issue is whether parallelograms, which have two pairs of parallel sides, should be counted as trapezoids. Some authors define a trapezoid as a quadrilateral having exactly one pair of parallel sides, thereby excluding parallelograms. Other authors define a trapezoid as a quadrilateral with at least one pair of parallel sides, making the parallelogram a special type of trapezoid (along with the rhombus, the rectangle and the square). The latter definition is consistent with its uses in higher mathematics such as calculus. The former definition would make such concepts as the trapezoidal approximation to a definite integral ill-defined.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by Alan3354(21580) About Me  (Show Source):
You can put this solution on YOUR website!
"Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, which statement must be true?"
A: Quadrilateral ABCD is a square
B: Quadrilateral ABCD is a rhombus
C: Quadrilateral ABCD is a rectangle
D: Quadrilateral ABCD is an isosceles trapezoid
I have eliminated "B" and "D", but I am unsure as to whether ABCD is square or rectangle. Could you kindly explain as to why it is either one?
----------------
A parallelogram's sides can be of unequal lengths, so it is not necessarily a square. That leaves rectangle.

Question 570599: If the area of a rhombus is 252 and the perimeter is 84, what is the altitude?
I have tried to use the area equation on A=1/2xy. I can not get it to work out. Please help.
Answer by Edwin McCravy(6932) About Me  (Show Source):
You can put this solution on YOUR website!
If the area of a rhombus is 252 and the perimeter is 84, what is the altitude?
The perimeter 84 is the sum of all 4 sides.  Since a rhombus has 4 equal sides,
each side is 1%2F4 of 84 or 21 each:  

drawing%28400%2C168%2C-5%2C45%2C-5%2C16%2C%0D%0Alocate%287%2C8%2C21%29%2Clocate%2810.5%2C0%2C21%29%2Clocate%2830%2C6.5%2C21%29%2Clocate%2825%2C14%2C21%29%2C%0D%0Aline%280%2C0%2C21%2C0%29%2C+line%2821%2C0%2C3sqrt%2833%29%2B21%2C12%29%2Cline%283sqrt%2833%29%2B21%2C12%2C3sqrt%2833%29%2C12%29%2C%0D%0Aline%283sqrt%2833%29%2C12%2C0%2C0%29+%29

Draw the altitude (in green), label it h:

drawing%28400%2C168%2C-5%2C45%2C-5%2C16%2Cgreen%28line%283sqrt%2833%29%2C12%2C3sqrt%2833%29%2C0%29%2Clocate%2817.5%2C7%2Ch%29%29%2C%0D%0Alocate%287%2C8%2C21%29%2Clocate%2810.5%2C0%2C21%29%2Clocate%2830%2C6.5%2C21%29%2Clocate%2825%2C14%2C21%29%2C%0D%0Aline%280%2C0%2C21%2C0%29%2C+line%2821%2C0%2C3sqrt%2833%29%2B21%2C12%29%2Cline%283sqrt%2833%29%2B21%2C12%2C3sqrt%2833%29%2C12%29%2C%0D%0Aline%283sqrt%2833%29%2C12%2C0%2C0%29+%29

The area of a parallelogram (and a rhombus IS a parallelogram) is

Area = base×altitude

The base is the bottom side or 21, the altitude is h and the area is 252.

 252 = 21×h
 
 252%2F21 = h
  12 = h

So the altitude is 12.

Edwin


Question 568657: The measure of angle A is 30 degrees less than twice the measures of angle B. Find the measures of each angle of the parallelogram
Answer by stanbon(48517) About Me  (Show Source):
You can put this solution on YOUR website!
The measure of angle A is 30 degrees less than twice the measures of angle B. Find the measures of each angle of the parallelogram
The measure of angle A is 30 degrees less than twice the measures of angle B. Find the measures of each angle of the parallelogram
---
I'll assume that A and B are consecutive angles of the parallelogram.
A and B are suppliemntary.
A + B = 180
A = 2B-30
--------------
2B-30+B = 180
3B = 210
B = 70 degrees
----
A = 180-70 = 110 degrees
------------------------------
Cheers,
Stan H.
-------------

Question 568071: is a quadrilateral with sides 5, 8, 5, 8 in that order always a rectangle?
Answer by richard1234(4789) About Me  (Show Source):
You can put this solution on YOUR website!
Not necessarily, maybe a parallelogram.

Question 568020: The sum of the angle measures of a polygon with n sides is 1080. Find n.
Answer by stanbon(48517) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the angle measures of a polygon with n sides is 1080. Find n.
----
sum = (n-2)180
1080 = (n-2)180
n-2 = 6
n = 8 sides
==============
Cheers,
Stan H.
============

Question 567134: How do you find the measurement or value of a parallelogram? i thought the opposite sides were suppost to be the same measurement but i guess not.
Answer by Edwin McCravy(6932) About Me  (Show Source):
You can put this solution on YOUR website!
They are. State the problem like it's stated in your book, and
we'll help you.

Question 566546: Quadrilateral abcd has vertices a(-5,6) b(6,6)c(8,3) and d(-3-3).
Prove quadrilateral abcd is a parallelogram but is neither a rhombus nor a rectangle.
Answer by solver91311(12121) About Me  (Show Source):
You can put this solution on YOUR website!


Using the vertex data given and the slope formula, calculate the slopes of the four lines that contain the side segments.



where and are the coordinates of the given points.

If it is a parallelogram, then the results of the first step will be that two of the lines have slopes equal to each other and the other two slopes are also equal to each other.

If the two non-equal slope numbers are not negative reciprocals, then the non-parallel sides are not perpendicular. (in this case, one of the slopes is zero, so if the lines were perpendicular, the other slope would be undefined) If the non-parallel sides are not perpendicular, then the figure cannot be a rectangle.

Use the distance formula



to calculate the measure of one of the sides. Then do it again for one of the sides not parallel to the first one. If the measures are different, the figure cannot be a rhombus.

By the way, label vertices with upper case and sides with lower case.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Question 566134: In Rhombus ADBC, point A is (6,13) on the coordinate plane, and point B is (13,6) Find the slope-intercept equation of diagonal CD in the rhombus.
Answer by Edwin McCravy(6932) About Me  (Show Source):
You can put this solution on YOUR website!
The rhombus could look like any of these, even the square on the right
(a square is a rhombus).  But regardless, the diagonal CD that goes up to
the right is always a segment of the same (green) line, and the green
line is always perpendicular to the red diagonal, because the diagonals
of a rhombus are perpendicular bisectors of each other.

drawing%28350%2C350%2C-2%2C20%2C-2%2C20%2C+graph%28350%2C350%2C-2%2C20%2C-2%2C20%29%2C%0D%0Alocate%282.5%2C13.5%2C%27A%286%2C13%29%27%29%2C+circle%286%2C13%2C.2%29%2C+green%28line%28-5%2C-5%2C25%2C25%29%29%2C%0D%0Alocate%2813.2%2C5.6%2C%27B%2813%2C6%29%27%29%2C+circle%2813%2C6%2C.2%29%2C+red%28line%286%2C13%2C13%2C6%29%29%2C%0D%0Aline%286%2C13%2C2.5%2C2.5%29%2C+line%2813%2C6%2C2.5%2C2.5%29%2C+line%286%2C13%2C16.5%2C16.5%29%2C+line%2813%2C6%2C16.5%2C16.5%29%2C+locate%282.5-.5%2C2.5%2CD%29%2C+locate%2816.5%2B.3%2C16.5%2B.5%2CC%29%0D%0A%0D%0A+%29drawing%28350%2C350%2C-2%2C20%2C-2%2C20%2C+graph%28350%2C350%2C-2%2C20%2C-2%2C20%29%2C%0D%0Alocate%282.5%2C13.5%2C%27A%286%2C13%29%27%29%2C+circle%286%2C13%2C.2%29%2Cgreen%28line%28-5%2C-5%2C25%2C25%29%29%2C%0D%0Alocate%2813.2%2C5.6%2C%27B%2813%2C6%29%27%29%2C+circle%2813%2C6%2C.2%29%2C+red%28line%286%2C13%2C13%2C6%29%29%2C%0D%0Aline%286%2C13%2C7.5%2C7.5%29%2C+line%2813%2C6%2C7.5%2C7.5%29%2C+line%286%2C13%2C11.5%2C11.5%29%2C+line%2813%2C6%2C11.5%2C11.5%29%2C+locate%287.5-.5%2C7.5%2CD%29%2C+locate%2811.5%2B.3%2C11.5%2B.5%2CC%29%0D%0A%0D%0A%0D%0A+%29drawing%28350%2C350%2C-2%2C20%2C-2%2C20%2C+graph%28350%2C350%2C-2%2C20%2C-2%2C20%29%2C%0D%0Alocate%282.5%2C13.5%2C%27A%286%2C13%29%27%29%2C+circle%286%2C13%2C.2%29%2Cgreen%28line%28-5%2C-5%2C25%2C25%29%29%2C%0D%0Alocate%2813.2%2C5.6%2C%27B%2813%2C6%29%27%29%2C+circle%2813%2C6%2C.2%29%2C+red%28line%286%2C13%2C13%2C6%29%29%2C%0D%0Aline%286%2C13%2C6%2C6%29%2C+line%2813%2C6%2C6%2C6%29%2C+line%286%2C13%2C13%2C13%29%2C+line%2813%2C6%2C13%2C13%29%2C+locate%286-.5%2C6%2CD%29%2C+locate%2813%2B.3%2C13%2B.5%2CC%29%0D%0A%0D%0A%0D%0A+%29

We first find the slope of the red diagonal:

Slope formula
m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 with (x1, y1) = (6,13) and (x2, y2) = (13,6)

m = %28%286%29-%2813%29%29%2F%28%2813%29-%286%29%29 = %28-7%29%2F%287%29 = -1

The slope of the green line will have the slope that is formed by
inverting %28-1%29%2F1 as 1%2F%28-1%29 or -1 and changing the sign to +1

So the slope of the desired green line is +1.

Now we need a point that it goes through.  Since the diagonals of any
parallelogram bisect each other, we must find the midpoint of the red
diagonal.

Midpoint formula:
 
Midpoint = %28matrix%281%2C3%2C++++++%28x%5B1%5D%2Bx%5B2%5D%29%2F2%2C+++%27%2C%27%2C+%28y%5B1%5D%2By%5B2%5D%29%2F2%29%29 
 
Midpoint = %28matrix%281%2C3%2C++++++%28%286%29%2B%2813%29%29%2F2%2C+++%27%2C%27%2C+%28%2813%29%2B%286%29%29%2F2%29%29
 
Midpoint = %28matrix%281%2C3%2C++++++19%2F2%2C+++%27%2C%27%2C+19%2F2%29%29   

Now we use the point-slope formula:

y - y1 = m(x - x1)

y - 19%2F2 = 1(x - 19%2F2)

y - 19%2F2 = x - 19%2F2

     y = x

So that's the answer, the equation of the green line.

Edwin

Question 566083: what is 5y-7
Answer by Alan3354(21580) About Me  (Show Source):
You can put this solution on YOUR website!
what is 5y-7
----------
It's a binomial.

Question 565849: How do you find the perimeter of a parallelogram (square, rectangle, or rhombus) when you are only given some numbers in the problem?
Answer by ad_alta(170) About Me  (Show Source):
You can put this solution on YOUR website!
Squares and rhombi are easy, since all the sides have equal length. If you have one side, just multiply by 4. For a rectangle add twice the width to twice the height.

Question 565817: my homework is asking me: For what values of x and y must each figure be a parallelogram?
1. it is a rhombus with 4y , x , 2y, and (5x-180) in each corner. (angle measures)
i tried to create a problem by doing 6y+6x-180=180 but it didn't work out and i don't know any other way to do it. can you please help thank you :)
Answer by mananth(10541) About Me  (Show Source):
You can put this solution on YOUR website!
The interior angles of a parallelogram add up to 180 deg
4y+x=180
2y+5x-180=180
2y+5x=360

4y+x=180
2y+5x=360 multiply the equation by -2 and to the other equation
-4y-10x=-720
-9x=-540
/-9
x=54
solve for y
4y+x=180
4y+54=180
4y=136
/4
y=39

Question 565639: how is finding the area of a parallelogram similar to finding the are of a rectangle ?
Answer by stanbon(48517) About Me  (Show Source):
You can put this solution on YOUR website!
how is finding the area of a parallelogram similar to finding the are of a rectangle ?
----
For both, Area = (base)(height)
================================
Cheers,
Stan H.

Question 565616: if a figure is a parallelogram it cannot be a __________________

Answer by stanbon(48517) About Me  (Show Source):
You can put this solution on YOUR website!
if a figure is a parallelogram it cannot be a circle.
------------

Question 565384: The measure of one angle of a parallelogram is 39. Which of theses
is the measure of another angel in the
Parallelogram
A. 51
B. 141
C. 107
D. 282
Answer by stanbon(48517) About Me  (Show Source):
You can put this solution on YOUR website!
Ans: 141 because adjacent angles are supplementary.
Cheers,
Stan H.

Question 563081: Can u tell me the formulae for finding area of parallelogram with 4 coordinates?
Answer by richard1234(4789) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose the coordinates are (0,0), (a,b), (c,d) and (a+c,b+d) (we may assume one of the coordinates is (0,0) in order to fix a point). Then the area is equal to the determinant of the matrix
|a b|
|c d|

or ad-bc.

Question 563124: what is the perimeter of a parallelogram that is 30 cm by 20cm?

Answer by richard1234(4789) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter = 30+30+20+20 = 100 cm

Question 562586: I need help with quadrilaterals!
Answer by solver91311(12121) About Me  (Show Source):
You can put this solution on YOUR website!


We will alert the media. Meanwhile, if you want a meaningful answer, ask a specific question. Go back and re-read the instructions for posting.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Question 559506: If you are just given vertices how do you find out if the shape is a rhombus, a rectangle, or a square?
Answer by KMST(586) About Me  (Show Source):
You can put this solution on YOUR website!
Calculating the lengths of the diagonals and checking if they are perpendicular would help you.
A rhombus has perpendicular diagonals.
A rectangle has diagonals of the same length.
A square has perpendicular diagonals with the same length. (It can be considered a special kind of rhombus. It can also be considered a special kind of rectangle).

Question 558828: in the given figure, ABCD is a parallelogram with perimeter 4o cm,AD=2x, CD=2y+2, AB=3x. Find the value of x and y.

Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
First of all, AD=BC, so BC also is 2x.

Secondly, AB=CD, so 3x=2y+2. If you solve for 2y, 2y=3x-2

Thirdly, Perimeter = Sum of four sides
2x+3x+2x+2y+2 = 40

Simplify:
7x+2y+2=40

Substitute 2y=3x+2:
7x + 3x-2+2=40
10x=40
x=4

2y=3x-2
2y=3*4-2
2y=10
y=5

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

Question 557284: Given ABCD is a parallelogram, angle A= (x+6)degrees, and angle B= (2x+15)degrees,then find the measure of angle D.
A) 21
B) 127
C) 53
D) 121
Answer by heilok(4) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,

Here are a few reminders about solving the problem:
1) angle sum of parallelogram=360 degrees
2) opposite angles of parallelogram are equal in size
3) sum of interior angles of parallelogram=180 degree

Very unfortunately, the question didn't tell you whether angle A and angle B are a pair of opposite angles or interior angles. So you need to try it out yourself.

Firstly, assume angle A and angle B are a pair of opposite angles. Therefore,

x+6=2x+15
2x-x=6-15
x=-9.

However, let's calculate the size of angle A in this case.

Sub x=-9,
angle A=x+6
=-9+6
=-3 ,which is impossible to be an angle.
Now ,the conclusion is: angle A and angle B are a pair of interior angles. Therefore,
(x+6)+(2x+15)=180
3x=180-21
x=53

so,angle A=x+6
=59.





If angle A and angle D are a pair of opposite angles,
Therefore angle A=Angle D
Angle D=x+6
=53+6
=59


If angle A and angle D are a pair of interior angles,

Therefore angle A+Angle D =180
59+angle D = 180
Angle D=121

Angle D can be 59 or 121 degrees.
Ans. D

Cheers,
Heil

Question 557093: in a parallelogram one side is 13 meter and another is 11 meters and one of the diagonals is 16 meters.
find the other diagonal
Answer by Theo(2967) About Me  (Show Source):
You can put this solution on YOUR website!
http://www.math10.com/en/geometry/parallelogram.html>
the answer to your question lies in the reference.
if you allow a and b to be equal to the sides of your parallelogram, and if you allow p and q to be equal to the diagonals of your parallelogram, then the relationship between the sides and the diagonals is given by the formula:
p^2 + q^2 = 2 * (a^2 + b^2)
in your parallelogam, you can assign values as follows:
a = 13
b = 11
p = 16
q = x
the formula becomes:
16^2 + x^2 = 2 * (13^2 + 11^2)
simplify to get:
256 + x^2 = 2 * (169 + 121)
simplify further to get:
256 + x^2 = 580
subtract 256 from both sides of this equation to get:
x^2 = 580 - 256 which becomes:
x^2 = 324
take the square root of both sides of this equation to get:
x = 18
that's your answer.
the length of the other diagonal is equal to 18 meters
-----
if you did not know the formula, then you could have found it the hard way by using the pythagorean formula on right triangles formed from the parallelogram. i did it that way to convince myself that i could get the same answer. i did get the same answer, so i'm comfortable with the formula. using the formula is much easier.


Question 556782: ABCD is a quadrilateral with AB = 8, BC = 13 and DC = 15. What is the maximum possible integral value of AD?
Answer by mathstutor494(92) About Me  (Show Source):
You can put this solution on YOUR website!
Ans = 35
If you need more help, email me at mathstutor494@gmail.com

Question 556153: Qhen finding the measure of the interior angle and finding X how do you find
J,K,L,M If J=(3x-6) K=(x+10) L=2x and M=(2x-8)?
i used the equation-n-2(180) add up all my x's and numbers and got 8x-4=360
+4 +4 and got 8x=364 then divided that by 8 to get X=44.5
Answer by KMST(586) About Me  (Show Source):
You can put this solution on YOUR website!
You got it right. You could go a little further and calculate the angles if needed.
If JKLM is a polygon, it has 4 sides/4 angles, so n=4, and the sum of its interior angle measures (in degrees) is n-2(180) = 2(180) = 360.
With J=3x-6, K=x+10, L=2x, and M=2x-8, your equation would start as
(3x-6)+(x+10)+2x+(2x-8) = 360
It would simplify into
8x-4 = 360
and the solution would be x=45.5 as you said,
Then, you could calculate the measures of the angles (in degrees):
J = 3x-6 = 3(45.5)-6 = 136.5 - 6 = 130.5 = 130 degrees 30 minutes
K = x+10 = 45.5 + 10 = 55.5 = 55 degrees 30 minutes
L = 2x = 2(45.5) = 91
and M = 2x-8 = 2(45.5) - 8 = 83

Question 555967: The questions asks:
What is the most precise classification of this quadrilateral which has opposite sides with equal slopes and consecutive sides with slopes that are negative reciprocals?
I have tried to graph things that would work and thought of the descriptions of the geometric shapes, but I just can't seem to find one that fits this description.
Answer by KMST(586) About Me  (Show Source):
You can put this solution on YOUR website!
If opposite sides have equal slopes they are parallel.
That makes your quadrilateral a parallelogram.
If consecutive sides have slopes that are negative reciprocals, that makes them perpendicular.
A parallelogram with right angles is called a rectangle.

Question 555191: My question is:
Graph the point A(3,2), B(1,-2), C(2, -5), D(4,-1) on the coordinate plane. What kind of quadrilateral is ABCD? Use math to justify your answer.
I did the graph and it looks like a parrallelagram, but I do not know how to justify this if it is correct.
Answer by Alan3354(21580) About Me  (Show Source):
You can put this solution on YOUR website!
My question is:
Graph the point A(3,2), B(1,-2), C(2, -5), D(4,-1) on the coordinate plane. What kind of quadrilateral is ABCD? Use math to justify your answer.
I did the graph and it looks like a parrallelagram, but I do not know how to justify this if it is correct.
----------
If AB is parallel to CD and AD parallel to BC, it's a parallelogram.

Question 554587: Find the values of X and Y in parallelogram ABCD.
AB - 2y, BC = y + 1, CD = 5x - 1, DA - 2x + 4

I'm totally stuck.
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: This is a parallelogram, so the opposite sides are equal. This means that

AB = CD and BC = DA


giving us the two equations


2y = 5x-1 and y+1 = 2x+4


Use either substitution, elimination, or graphing to solve.

Question 554341: Suppose two distinct parallelograms lie in a plane. What is the LARGEST number of points at which they can intersect?
The answer choices are: 2, 4, 6, & 8.
I was thinking it was either 2 or 4, but I just can't remember. I've looked everywhere in my notes, and Google is kind of useless :(
Thank you!!
Found 2 solutions by richard1234, Edwin McCravy:
Answer by richard1234(4789) About Me  (Show Source):
You can put this solution on YOUR website!
You can't really guess at it, and notes or Google won't help for this type of question. I would draw something like what the other tutor drew. Note that you can rigorously prove that the answer is at most 8 (presuming no two segments of different parallelograms are the same), but we don't need to go there.

Answer by Edwin McCravy(6932) About Me  (Show Source):
You can put this solution on YOUR website!


It's like the red square and the green square below.  Squares ARE

parallelograms, by the way.  So the answer is ---- (you count 'em):



drawing%28400%2C400%2C-3%2C3%2C-3%2C3%2C%0D%0A%0D%0Ared%28line%28-2%2C2%2C2%2C2%29%2Cline%282%2C2%2C2%2C-2%29%2Cline%282%2C-2%2C-2%2C-2%29%2Cline%28-2%2C-2%2C-2%2C2%29%29%2C%0D%0A%0D%0Agreen%28line%28-3%2C0%2C0%2C3%29%2Cline%280%2C3%2C3%2C0%29%2Cline%283%2C0%2C0%2C-3%29%2Cline%280%2C-3%2C-3%2C0%29%29%0D%0A+%0D%0A%29



Edwin

Question 553096: Determine whether the figure with the given vertices is a parallelogram. Use the method of the Distance and Slope Formula.
R (-2, 5)
O (1, 3)
M (-3, -4)
Y (-6, -2)
Answer by solver91311(12121) About Me  (Show Source):
You can put this solution on YOUR website!


Use the slope formula:


where and are the coordinates of the given points.

To calculate the slopes of the lines containing the four segments RO, OM, MY, and YR. If ROMY is a parallelogram, then slope RO = slope MY and slope OM = slope YR.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Question 551992: Could you please help me solve this...
The sides of a rectangle are A: 5X, B:5Y, C:7Y+7, D: 2X+6
What are the values of the variables and the length of the sides.
Answer by Theo(2967) About Me  (Show Source):
You can put this solution on YOUR website!
your rectangle is:
ABCD
side AB is equal to 5x.
side BC is equal to 5y.
side CD is equal to 7y+7
side AD is equal to 2x+6
side AB is opposite side CD.
side BC is opposite side AD
opposite sides of a rectangle are equal.
this means that:
5x = 7y+7
5y = 2x+6
solve for y in each equation to get:
y = (5x-7)/7 (first equation)
y = (2x+6)/5 (second equation)
since they are both equal to y, then they are both equal to each other and we get:
(5x-7)/7 = (2x+6)/5
multiply both sides of this equation by 35 to get:
5(5x-7) = 7(2x+6)
simplify to get:
25x - 35 = 14x + 42
subtract 14x from both sides of this equation and add 35 to both sides of this equation to get:
11x = 77
divide both sides of this equation by 11 to get:
x = 7
substitute for x in either original equation to get:
y = 4
your solution is that x = 7 and y = 4.
you confirm by substituting for x and y in each original expression of the rectangle to get:
AB = 5x = 5*7 = 35
BC = 5y = 5*4 = 20
CD = 7y + 7 = 7*4 + 7 = 28 + 7 = 35
AD = 2x + 6 = 2*7 + 6 = 14 + 6 = 20
we know that AB is supposed to be equal to CD and BC is supposed to be equal to AD.
we get:
35 = 35 for AB equal to CD and we get:
20 = 20 for BC equal to AD.
everything checks out so the values of x and y are good.

Question 551331: In parallelogram ABCD, if the measure of angle A is 5x+30, and the measure of angle D is x, find the measure of angle C.
Answer by Theo(2967) About Me  (Show Source):
You can put this solution on YOUR website!
angle A is supplementary to angle D (adjacent angles of a parallelogram).
this means that:
5x + 30 + x = 180
combine like terms and subtract 30 from both sides of the equation to get:
6x = 150
divide both sides of the equation by 6 to get:
x = 25
angle C is equal to angle A.
angle A is equal to 5x + 30 = 125 + 30 = 155.
angle C is therefore equal to 155 degrees.
in a parallelogram:
opposite angles are equal.
adjacent angles are supplementary.
this makes angle A equal to angle C and supplementary to B and D which makes angle B equal to angle D.

Question 550573: LM is the midsegment of trapezoid ABCD. AB=x+8, LM=4x+3, and DC=187. What is the value of x? Please explain not sure how to work this out.
Found 2 solutions by solver91311, mathstutor494:
Answer by solver91311(12121) About Me  (Show Source):
You can put this solution on YOUR website!


The measure of the midsegment (the segment whose endpoints are the midpoints of the non-parallel sides of the trapezoid) of a trapezoid is the average of the measures of the two parallel sides.

The two parallel sides are and , so the average is which, according to the givens is:



And this average has to be equal to the given measure of the midsegment, so:



Solve for .

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by mathstutor494(92) About Me  (Show Source):
You can put this solution on YOUR website!
Length of the midsegment of a trapezoid is the average length of the bases,
i.e. LM = (AB+DC)/2
Substituting the values given, we get
4x+3 = ((x+8)+187))/2
Multiplying both sides by 2 ...
> 2*(4x+3) = ((x+8)+187))
> 8x+6 = x+195
> 8x-x = 195-6
> 7x = 189
> x = 27 ( Dividing both sides by 7)

Question 550000: Verify that parallelogram ABCD with vertices A(–5, –1), B(–9, 6), C(–1, 5), and D(3, –2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals
Answer by josmiceli(6781) About Me  (Show Source):
You can put this solution on YOUR website!
If I choose pairs of points, and the parallelogram
is a rhombus, the slopes of the lines through
these pairs of points will either be parallel
or they will be negative reciprocals of
each other ( perpendicular )
-----------------------
If will choose the pairs
(1) A(-5,-1) and C(-1,5)
and
(2) B(-9,6) and D(3,-2)
--------------------
The slope of pair (1) is
( change in y ) / ( change in x ) = +%285+-%28-1%29%29+%2F+%28-1+-%28-5%29%29+=+6%2F4+
+6%2F4+=+3%2F2+
The slope of pair (2) is
( change in y ) / ( change in x ) = +%28+-2+-+6+%29+%2F+%28+3+-%28-9%29+%29+=+-8%2F12+
+-8%2F12+=+-2%2F3+
----------------
These lines have slopes that are negative reciprocals of each other,
so they are perpendicular, and the parallelogram is a rhombus
----------------
You can also show ( not necessary ) that the pairs of
points AB and CD form lines which are parallel

Question 549946: Find an equation in slope-intercept form passing through the points (2,5) and (7,-3).

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=2 and y%5B1%5D=5.
Also, is the second point . So this means that x%5B2%5D=7 and y%5B2%5D=-3.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-3-5%29%2F%287-2%29 Plug in y%5B2%5D=-3, y%5B1%5D=5, x%5B2%5D=7, and x%5B1%5D=2


m=%28-8%29%2F%287-2%29 Subtract 5 from -3 to get -8


m=%28-8%29%2F%285%29 Subtract 2 from 7 to get 5


So the slope of the line that goes through the points and is m=-8%2F5


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-5=%28-8%2F5%29%28x-2%29 Plug in m=-8%2F5, x%5B1%5D=2, and y%5B1%5D=5


y-5=%28-8%2F5%29x%2B%28-8%2F5%29%28-2%29 Distribute


y-5=%28-8%2F5%29x%2B16%2F5 Multiply


y=%28-8%2F5%29x%2B16%2F5%2B5 Add 5 to both sides.


y=%28-8%2F5%29x%2B41%2F5 Combine like terms. note: If you need help with fractions, check out this solver.



So the equation that goes through the points and is y=%28-8%2F5%29x%2B41%2F5

Question 549542: Which of the following conditions or set of conditions is sufficient for a parallelogram to be a square?
Answer by richard1234(4789) About Me  (Show Source):
You can put this solution on YOUR website!
The only conditions required are that the parallelogram has four congruent sides (or equivalently, equal diagonals) and four right angles.

Question 549945: The points (1,5), (4,5), and (1,0) represent three corners of a rectangle; find the coordinates of the fourth point.

Answer by asuar010(102) About Me  (Show Source):
You can put this solution on YOUR website!
the other point should be at (4,0). This can be verified by plotting them in graph paper.

Question 548775: Which is NOT always a property of a Parallelogram?
A. Diagonals that bisect each other
B. Diagonals that bisect opposit angles
C. Two pairs of opposite congruent sides
D. Two pairs of opposite congruent angles
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
The answer is B. Diagonals that bisect opposit angles


Draw a very elongated rectangle and draw in a diagonal and you'll see that the angles aren't cut in half.

Question 548022: a four-sided polygon that has these side lengths: 3 inches, 5 inches, 3 inches, and 5 inches. ron says it must be a rectangle. hermione says not necessarily. why is hermione right?
Answer by Alan3354(21580) About Me  (Show Source):
You can put this solution on YOUR website!
It could be a parallelogram.
The 2 5 inch sides could be adjacent, then it's just an irregular polygon.

Question 547308: Is the figure U a parallelogram. My daughter says yes but I say no because there are not 4 sides. Please explain tried to research but no answer came back.
Thanks
Answer by richard1234(4789) About Me  (Show Source):
You can put this solution on YOUR website!
The letter "U" is not a parallelogram. A parallelogram (or any polygon) is a closed shape.

Question 545982: I'm having trouble with a word problem.
A rectangular family room is twice as long as it is wide, and its area is 98 square feet. Find the dimensions of the family room.
Found 2 solutions by JBarnum, stanbon:
Answer by JBarnum(1826) About Me  (Show Source):
You can put this solution on YOUR website!
L%2AW=A formula
A=98 area given
L=2W length given
2W%2AW=98 substitution
2W%5E2=98solve for W
W%5E2=49 take sqrt
highlight%28W=7%29
L=2%287%29
highlight%28L=14%29
check
7%2A14=98
98=98
correct

Answer by stanbon(48517) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular family room is twice as long as it is wide, and its area is 98 square feet. Find the dimensions of the family room.
----
Let width be "x".
Then length is "2x".
------
Equation:
x*(2x) = 98
2x^2 = 98
x^2 = 49
x = 7 ft. (width)
2x = 14 ft. (lenght)
======================
Cheers,
Stan H.
======================

Question 545533: in rhombus ABCD, the measure of angle A and the measure of angle B are in the ratio 2:1, AB= 2x+8, BC= 5x+10.
i dont know what to do. i tried drawing it on a piece of paper but I dont know what im suposed to do.
Answer by KMST(586) About Me  (Show Source):
You can put this solution on YOUR website!
drawing%28200%2C200%2C-2%2C2%2C-2%2C2%2C%0D%0Atriangle%280%2C-1%2C0%2C1%2C1.73%2C0%29%2C+triangle%280%2C-1%2C0%2C1%2C-1.73%2C0%29%2C%0D%0Alocate%280%2C-1%2CC%29%2C+locate%281.8%2C0%2CB%29%2C%0D%0Alocate%280%2C1.5%2CA%29%2C+locate%28-2%2C0%2CD%29%0D%0A%29 seems to be a good depiction of your rhombus (two equilateral triangles stuck together).
I do not know what the question is. Find x? Find AB and BC? Find AC?
I do not know what the angles have to do with whatever the question could be.
In a rhombus, all 4 sides have the same length, so
2x%2B8=5x%2B10 --> 8=5x-2x%2B10 --> 8=3x%2B10 --> 8-10=3x --> -2=3x --> x=-2%2F3
So AB=2x%2B8=2%2A%28-2%2F3%29%2B8=-4%2F3%2B24%2F3=20%2F3
BC should be the same, let's verify, and see if I did calculations right.
BC=5x%2B10=5%2A%28-2%2F3%29%2B10=-10%2F3%2B30%2F30=20%2F3
If they ask about AC, that's where the angles would do something. As the measure of angle A (angle DAB, made of congruent angles DAC and CAB) is twice the measure of angle B (angle ABC), angles CAB, and ABC are congruent (and so is BCA, because the rhombus is symmetrical). That makes the two triangles ABC and ACD equilateral, and that's how you know that AB=BC=AC=20/3.

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810