Questions on Geometry: Parallelograms answered by real tutors!

Tutors Answer Your Questions about Parallelograms (FREE)

Question 750492: Parallelogram ABCD has obtuse angles that are twice as big as the acute angles. What is the measurement of each acute angle?
Answer by jim_thompson5910(28504)

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Let x = measure of acute angle, so 2x is the obtuse angle (since it's twice as big). Adjacent angles in a parallelogram add to 180 degrees, so we can say

x + 2x = 180 ... now solve for x

3x = 180

x = 180/3

x = 60

2x = 2*60

x = 120

So the obtuse angles are 120 degrees and the acute angles are 60 degrees

Question 749393: two vertices of a square are (-4,3) and (3,3). what two sets of coordinates could form the other vertices? A)(-4,8) and (3,8) B)(-4,-4) and (3,-4)
C)(4,8) and (-3,8) D)(-4,4) and (4,-4)
Answer by lynnlo(4155)

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Question 748337: Is a trapezoid a parallelogram?

Answer by tommyt3rd(455)

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No. A parallelogram is a quadrilateral with 2 pairs of parallel sides a trapezoid only has 1 pair

:)

Question 747973: If three corners of a parallelogram are (1,1), (4,2) and (1,3) then the fourth corner is........
Answer by Edwin McCravy(8882)

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This problem has three different solutions:



Here they are:

    

The points circled in blue are the solutions.  I'll let you get the
coordinates of those three points.

If you were to put all three solutions on the same graph, you'd get 
what's below, which is quite interesting that you get a big triangle
with a small triangle inside whose vertices are the three given points,
and they are the midpoints of the sides of the big triangle:



Edwin

Question 747785: A square is divided into three equal area by two parpllel lines drawn from opposite vertices.Determine the square in cm square if the distance between the two lines is 1 cm ?
Answer by lynnlo(4155)

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Question 746953: what equation represents a line that is perpendicular to the graphed line and passes through the point (2,5)

Answer by Alan3354(30983)

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what equation represents a line that is perpendicular to the graphed line and passes through the point (2,5)
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No graph is shown.

Question 746523: A hexagon has all sides at 5x and a triangle next to it are x+14, x+17, and 8x+9
Answer by Alan3354(30983)

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A hexagon has all sides at 5x and a triangle next to it are x+14, x+17, and 8x+9
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That's interesting (not really).

Question 746030: "Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the forth vertex."
(-4,8) Top left
(2,6) top right
(?, ?) bottom left
(5,-3) bottom right
Answer by Edwin McCravy(8882)

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"Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex."
(-4,8) Top left
(2,6) top right
(?, ?) bottom left
(5,-3) bottom right

Next we draw a horizontal (red) line from (2,6) left until we are directly
below the point (-4,8):

Next we draw a vertical (red) line up to the point (-4,8):

Now observe, by counting blocks, (1) that the horizontal red line goes
6 units left of (2,6), and that (2) the vertical line goes 2 units up
to the point (4,8).
Next, we do the same thing at the lower right point (5,-3).
We draw a red horizontal line 6 uints left of (5,-3) and then
2 unites upward, like this:

By counting blocks we see that that red vertical line ended up at (1,1),
so that's the answer. Now we can draw in the complete parallelogram:

Edwin

Question 745773: Hello, I have this problem where in a parallelogram, one obtuse angle = 225-2x. The x variable represents an acute angle. As you know all the angles of a quadrilateral added up equals 360 degrees. And the angles opposite eachother are equal. I have tried inputting some angles for x such as 45, 35, and 25 but none have worked. Please get back to me ASAP!! I need to know how to figure it out for a test tomorrow! ~Dani
Answer by KMST(1868)

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As you said, two of the angles will measure 225-2x

degrees.
If each of the other two angles measures

degrees,
as we know that the measures of all four angles add up to 360%5Eo

-->

-->

-->

-->

-->

-->

Question 745506: EF is a median of a trapezoid ABCD. AB equals 3x-1, EF equals 10, and DC equals 7x+1. What is the value of x
Answer by savvyhush23(50)

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Assuming that AB and DC is the bases of a trapezoid,
The median is: m=%28base1%2Bbase2%29%2F2

Therefore, x = 2

Question 745306: The area of parallelogram ABCD in square units is given by the polynomial x2 + 12x + 27. If DC¯¯¯¯¯ has length x + 9 units, find an expression for the height DE¯¯¯¯¯¯ .
Answer by stanbon(57246)

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The area of parallelogram ABCD in square units is given by the polynomial x2 + 12x + 27. If DC¯¯¯¯¯ has length x + 9 units, find an expression for the height DE¯¯¯¯¯¯ .
-----
Divide the quadratic by x+9
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(x^2 + 12x + 27)/(x+9) = x+3
============================
cheers,
Stan H.
===================

Question 743030: Are you a homosexual?

Answer by stanbon(57246)

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Question 742132: The coordinates of 3 of the vertices of a parallelogram are (–3, 4), (–2, 1), and (2, 6). What is the equation for the line containing the side opposite the side containing the first two vertices?
Answer by KMST(1868)

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The slope of the line connecting (-3,4) and (-2,1) can be calculated as the difference of the y-coordinates divided by the difference of the x coordinates.
Subtracting the coordinates of (-3,4) minus the coordinates of (-2,1), we get
slope=m=%284-1%29%2F%28-3-%28-2%29%29=3%2F%28-3%2B2%29=3%2F%28-1%29=-3

slope=m=%284-1%29%2F%28-3-%28-2%29%29=3%2F%28-3%2B2%29=3%2F%28-1%29=-3

The opposite side is parallel, and parallel lines have the same slope, so the line we want also has slope m=-3

.

The equation of a line with slope

and passing through point (2,6) can be written in point-slope form as
y-6=-3%28x-2%29

The more traditional (and unique) slope-intercept form of the equation can be derived from the point-slope form above.
y-6=-3%28x-2%29

-->

-->

-->

Question 741775: How would i figure out what FG is in this question? picture link below
http://static.panoramio.com/photos/1920x1280/89311946.jpg
Answer by lynnlo(4155)

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Question 741773: how would i solve this question?
http://static.panoramio.com/photos/1920x1280/89311946.jpg
Answer by lynnlo(4155)

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Question 739532: One Side of a Parallelogram is 16 cm. and its perimeter is 48 cm. find the lenght of the remaining side
Answer by KMST(1868)

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One side of a parallelogram has a length of 16cm.
The side parallel to that one, also has a length of 16 cm,
and the length of each of the other two sides is

cm.
The perimeter (in cm) is
16%2Bx%2B16%2Bx=48

-->

-->

-->

-->

-->

The other side length is 8cm.

Question 738475: if QRST is a rectangle find X if angle Q is equal to 10x-80
Answer by MathLover1(6622)

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if QRST is a rectangle, then each angle is

°
so, angle Q=90

°
if angle

is equal to 10x-80

, then

.....solve for

Question 737946: What is more than half of ten?

Answer by lynnlo(4155)

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6

Question 737873: The vertices of a figure are labeled clockwise A(–4, 2), B(2, 4), C(7, 1), and D(–5, –3). How could you show that the figure is a trapezoid? (Hint: A trapezoid has exactly one pair of parallel sides.
Answer by josgarithmetic(1482)

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That's it. You have the correct idea. Their slopes are equal.

Question 734102: in a plane, a set of 15 parallel lines intersects another set of 20 parallel lines to form parallelograms.
find the number of parallelograms formed.

Answer by KMST(1868)

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With so many parallel lines the number of parallelograms formed is very large.
for each parallelogram, two of the sides will be part a pair of parallel lines from the set of 15 parallel lines, and the other two sides will be part aother pair of parallel lines from the set of 20 parallel lines.
From the set of 15 parallel lines we can make 15%2A14%2F2=105

From the set of 20 parallel lines we can make 20%2A19%2F2=190

Since each of the 105

choices for one pair of sides can be paired with any of the 190

choices for the other pair of sides, the total number of parallelograms formed is
105%2A190=highlight%2819950%29

Question 733662: IN A PARALLELOGRAM ABCD ANGLE A=50DEGREE B=? HOW TO FIND IT
Answer by MathLover1(6622)

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In a parallelogram, adjacent angles add to 180

degrees

.....if

, then

Question 731845: Ashley wants to use the pattern shown below in her kitchen. The pattern is made up of parallelogram shaped tiles. work out the total area covered by the black tiles. give your answer in cm^2. this is a non calculator question... 2 parallelograms are 200 cm there's a space next to the parallelogram..... then a right angles triangle with a height of 260 cm.

Answer by lynnlo(4155)

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Question 731241: Find the value of each variable in the parallelogram. m∠1 = 10x, m∠2 = x + y, and m∠3 = 18z. http://www.phschool.com/atschool/phmath/tests/afa-06_assets/lesson4_qu1.gif
Answer by KMST(1868)

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The little marks across the sides mean that all sides are congruent.
That means it is a rhombus and the diagonals are perpendicular bisectors of each other.
All those angles are right angles.
The measures of those angles must be in degrees and the equations are
90=10x

and

-->

-->

-->

-->

-->

-->

Question 730006: given parallelogram PERT solve for x
angle P is (83-x)degrees
Angle E is 109 degrees
Angle T is also 109 degrees
Angle R is (5x+11)degrees
what is x?
Found 2 solutions by solver91311, lynnlo:
Answer by solver91311(16868)   (Show Source):
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Since E and T have the same measure P and R must have the same measure, so:

Solve for

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Answer by lynnlo(4155)   (Show Source):
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Question 730027: Find measures of ABCD
A=2x+3 B=? C=4x-10 D=3x+7
Answer by Alan3354(30983)   (Show Source):
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Find measures of ABCD
A=2x+3 B=? C=4x-10 D=3x+7
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How are they related?

Question 730036: The bases of two parallelograms are the same length. The height of the first parallelogram is half the height of the second.What is the ratio of the area of the first parallelogram to the area of the second? Justify your answer.
Answer by lynnlo(4155)   (Show Source):
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Question 729306: Find measurement angle PRS in square PQRS.
Answer by MathLover1(6622)   (Show Source):
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measurement angle PRS in square PQRS:
you already know that square has four right angles; so, angle PRS in square PQRS is °

Question 729384: PQRS is a parallelogram pq =5cm,qr=4cm,pr=6cm find the length of the perpendicular drawn from q to pr {in,cm}
Answer by lynnlo(4155)   (Show Source):
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Question 727710: In parallelogram ABCD, AB=2x-7, BC=x+3y, CD=x+y, and AD=2x-y-1. Please find x and y.
Answer by mbmodak(32)   (Show Source):
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https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQ7406FcocKuV2BVB0uES8BpiHy_EVmnoXmw26eRsOsUAEFJbKccw site for parallelogram ABCD
in which side ab // cd & ab=cd (opp.sides of paralleogram),bc //ad &bc=ad (opp.sides of paralleogram)
Ab=cd 2x-7=x+y ---(1) 2x-x-y=7 or x-y=7 (3)
bc=ad x+3y=2x-y-1 (2) x-2x+3y+y=-1 or -x+4y=-1 or x-4y=1 (4)
solve these(3) &(4) two linear equations
x-y =7 (3)
x-4y =1 (4) Subtract(4)-(3)
- + -
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3y = 6 Or y=2 Substitute y=2 in (3) we get x-2=7 or x=9
Thus x=9 y=2
[ab 2*9-7=9+2 or 18-7 = 11 which are opp sides // &equal similarly bc &ad]

Question 726728: 1. A boat is heading across a river at a velocity of 25 mph. The river is flowing downstream at 10 mph. What is the actual velocity of the boat?
Answer by Alan3354(30983)   (Show Source):
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1. A boat is heading across a river at a velocity of 25 mph. The river is flowing downstream at 10 mph. What is the actual velocity of the boat?
-----------

v = sqrt(735)
v =~ 27.11 mi/hr
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PS Rivers always flow downstream

Question 726729: An airplane is flying due east at 340 km/hr. The wind is blowing 40 km/hr at 34 degrees Southeast. What is the planes actual velocity?
Answer by Alan3354(30983)   (Show Source):
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An airplane is flying due east at 340 km/hr. The wind is blowing 40 km/hr at 34 degrees Southeast. What is the planes actual velocity?
-------------------
034 degs is not southeast, it's northeast.
Wind direction is the direction it's from.
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People should stick to writing problems that they know something about.

Question 726660: Side AB of parallelogram ABCD is represented by the equation y-7=3/2x. Which equation could represent side CD
Answer by jim_thompson5910(28504)   (Show Source):
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The slope of y-7=3/2x is 3/2 (since y-7=3/2x can be turned into y = 3/2x + 7)

So the slope of any equation going through CD must also have a slope of 3/2 because CD is parallel to AB and all parallel lines have the same slope.

So the answer will look like y = 3/2x + b where b is any number.

Question 726551: FIND THE VALUE OF X IN EACH PARALLELOGRAM

Answer by fcabanski(874)   (Show Source):
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There is not enough info to solve this problem.

Question 725141: Answer T or F.
_____ (a) Skew lines are coplanar. _____ (d) A circle is a polygon
_____ (b) A rhombus is always a parallelogram _____ (e) All parallelograms are squares
_____ (c) All trapezoids are rectangles _____ (f) A regular triangle is always isosceles

Answer by lynnlo(4155)   (Show Source):
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(A)FALSE
(2)TRUE
(3)FALSE
(4)FALSE
(5)TRUE
(6)TRUE

Question 724665: When trying to find the degree measure of an angle for a parallelogram with 2 given equations, do you set the equations equal to 180? If my question is unclear, here is a sample problem.
"The degree of m Would I do:
2x+10+3x=180
Or would I do:
2x+10+3x=360
Thanks!
Answer by solver91311(16868)   (Show Source):
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The sum of the measures of the interior angles of any quadrilateral is 360 degrees.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 724170: The measure of an angle of a parallelogram is 18 degrees less than 5 times the measure of an adjacent angle. Explain how to find the measures of all the interior angles of the parallelogram.
Answer by KMST(1868)   (Show Source):
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What you need to know is that the measures of adjacent interior angles of a parallelogram add up to . (We can be fancy and say that adjacent interior angles of a parallelogram are supplementary). With that, you set up an equation. The rest is simple algebra. Once you find one angle, the measures of the adjacent ones can be calculated by subtracting the measure found from , and the fourth angle has the same measure as the first one.

Angles 1 and 2 are adjacent interior angles of the blue parallelogram.

Let's sat that angle 1 measures degrees, and angle 2 measures "18 degrees less than 5 times the measure" of angle 1, so it measures degrees.
Since angles 1 and 2 are supplementary,
--> --> --> --> .
So angle 1 measures ,
the adjacent angles measure

WHY ADJACENT ANGLES ADD UP TO
In the drawing, angles 1 and 2 are adjacent interior angles of the blue parallelogram.
You might remember that when a line crosses two parallel line it forms eight angles, but among all those angles there will be at most two different measures, and measures that are not the same add up to .
In the drawing, the parallel horizontal lines and the slanted line that crosses them making the numbered angles, form a "family" of eight related angles. One half (four) of those angles are congruent to one another, and have the same certain measure, and the other group of four angles are also congruent to one another, and supplementary to the angles in the first group. So you have eight angles, but if you know the measure of one, you know the measure of all.
The pair of angles 2 and 3 are called vertical (to each other), and are known to be congruent (same measure). The same goes for angles 4 and 5.
The pair of angles 2 and 4 are called alternate interiors (to each other), and are also known to be congruent (same measure).
There are more names to describe the relation of one angle to another among those eight angles, but who needs to remember more names.
What matters is that angles 2, 3, 4, and 5 all have the same measure.
It is obvious that angles 4 and 5 are supplementary to angle 1.
Angle 2, having the same measure as 4 and 5, is also supplementary to angle 1.

Question 723802: Points A, B and C have the coordinates (1,6), (0,0) and (-2,2). Find 3 possible coordinates for a point D so that the four points form a parallelogram . Exclude the case where all points lie in a straight line. How do you work this out? Thanks, Lizzy.
Answer by josgarithmetic(1482)   (Show Source):
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The question is open ended, since there can be four other points to choose. Either imagine or plot on paper, the three given points, and choose where you wish to pick the fourth vertex of the parallelogram. This point will be an end point of a segment parallel to another defined line among your given set of points.

You may easily imagine the desired point directed from (1,6), and on a segment parallel to the line defined by (0,0) & (-2,2). Find the equation of the line with this slope and which contains (1,6).

You now want to get an equation of another line; the line has the same slope as the two points (0,0) & (1,6) but contains the point (-2,2).

ANSWER THIS QUESTION: At what point do these two lines intersect? THAT will be the point of the fourth vertex for one of the possible parallelograms.

Question 723062: Draw several parallelograms and measure sides. what can you conclude about opposite sides of a
Answer by fcabanski(874)   (Show Source):
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You're supposed to draw them and see for yourself that opposite sides of a parallelogram are parallel and congruent (equal in length).

Question 722681: How to find the area of the shaded region in a triangle if: You know that the triangle is composed of two smaller triangles. And, the first small triangle has the base of 5 and you don't know the height. You just know that the other side of the triangle measures 8. And the second smaller triangle has a base of 4....?
Answer by Edwin McCravy(8882)   (Show Source):
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How to find the area of the shaded region in a triangle if: You know that the triangle is composed of two smaller triangles. And, the first small triangle has the base of 5 and you don't know the height. You just know that the other side of the triangle measures 8. And the second smaller triangle has a base of 4....?

Use the Pythagorean theorem on the right triangle on the left to find h: c² = a² + b² 8² = 5² + h² 64 = 25 + h² 39 = h² √39 = h Now that we have the height, we can find the area. The whole base of the whole big triangle is 5+4 or 9 A = ·b·h A = ·9·√39 A = 28.10249099 [Round to the number of decimal places your teacher asks you to] Edwin

Question 721431: Are any types of parallelograms always similar?
Answer by Alan3354(30983)   (Show Source):
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Are any types of parallelograms always similar?
-----------
All squares are similar.

Question 717041: in the accompanying diagram of parallelogram ABCD, m angle B=5x, and m angle c=2x+12. Find the number of degrees in Is this the right approach?

then

and then angle d is equal or congruent to angle B so the answer is 140

Answer by lynnlo(4155)   (Show Source):
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Question 716743: Given the coordinates
M(-8,-1)
A(-2,5)
T(3,7)
H(-3,1)
- Plot the quadrilateral on the plane.
- Prove that the quadrilateral is a parallelogram. Use mathmatics to justify your answer.
- What special parallelogram is quadrilateral MATH?
Answer by Edwin McCravy(8882)   (Show Source):
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Given the coordinates
M(-8,-1)
A(-2,5)
T(3,7)
H(-3,1)
- Plot the quadrilateral on the plane.
-

Prove that the quadrilateral is a parallelogram. Use mathmatics to justify your answer.

Use the slope formula m = to show that MA ∥ HT To find the slope of MA Use (x₁,y₁) = (-8,-1) and where (x₂,y₂) = (-2,5) m = = = = 1 To find the slope of HT Use (x₁,y₁) = (-3,1) and where (x₂,y₂) = (3,7) m = = = = 1 So MA ∥ HT because the have the same slope of 1 each. -------------- Use the slope formula m = to show that MH ∥ AT To find the slope of MH Use (x₁,y₁) = (-8,-1) and where (x₂,y₂) = (-3,1) m = = = To find the slope of AT Use (x₁,y₁) = (-2,5) and where (x₂,y₂) = (3,7) m = = = So MH ∥ AT because the have the same slope of each. -----------------------------------------------------

- What special parallelogram is quadrilateral MATH?

This parallelogram is neither a rhombus nor a rectangle, so there is nothing special about this parallelogram other than the fact that its coordinates spell "MATH", and math happens to be the name of the subject you are studying. :) Edwin

Question 716163: Diagonal AC of a rhombus ABCD is equal to one of its sides BC. Find the angles of the
rhombus.
Answer by solver91311(16868)   (Show Source):
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If one of the diagonals is equal in measure to one of the sides, the rhombus must be formed from two equilateral triangles. Hence, the smaller angles are 60 degrees, and therefore the larger angles must be two times 60 or 120 degrees.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it