SOLUTION: A parallelogram whose diagonals are perpendicular is called a rhombus. Given the quadrilateral with vertices 𝐴 (−3,2),𝐵(−2,6), 𝐶(2,7),𝐷(1,3), a. Sketch the quadr

Question 1188582: A parallelogram whose diagonals are perpendicular is called a rhombus.
Given the quadrilateral with vertices 𝐴 (−3,2),𝐵(−2,6), 𝐶(2,7),𝐷(1,3),
a. Sketch the quadrilateral 𝐴BCD.
b. Verify that the quadrilateral ABCD is a parallelogram.
c. Verify that, in fact, it is a rhombus using the definition above.
d. Show that the rhombus can be subdivided into four right triangles.
e. Use part d. to find the area of the quadrilateral ABCD.
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
Sunday, April 2, 2017
7:06 PM

a. You can do your own sketch.

b. A quadrilateral is a parallelogram if the opposite sides are parallel. Line segments are parallel if the lines containing them are parallel. Lines are parallel if their slopes are equal.

Slope formula:

c. Line segments are perpendicular if the slopes of the lines containing them are negative reciprocals, that is their slopes are related as follows:

d. Perpendicular lines form four right angles. A right triangle contains exactly one right angle.

e. The area of a triangle is 1/2 times the base times the altitude. In a right triangle, the two legs are the base and the altitude. Use the midpoint formulas to find the coordinates of the intersection of the two diagonals and the distance formula to find the measure of the needed line segments.

Mid-point Formulas

Distance Formula

John

My calculator said it, I believe it, that settles it

From
I > Ø

RELATED QUESTIONS
If a Quadrilateral is a parallelogram with perpendicular diagonals then its a rhombus??? (answered by Mathtut)

prove that if the diagonals of a parallelogram are perpendicular, then the parallelogram... (answered by robertb)

2. Prove that the points (-2, 9), (-4, -2), (1, -12) and (3, -1) are vertices of a... (answered by jim_thompson5910)

Theorem 3. the diagonals of a rhombus are perpendicular. Given: Rhombus ROSE Prove:... (answered by ikleyn)

Verify that parallelogram ABCD with vertices A(�5, �1), B(�9, 6), C(�1, 5), and D(3, �2)... (answered by josmiceli)

Give a formal proof of the following theorem 1. A quadrilateral with one pair of... (answered by CPhill)

1.how to prove if the diagonals in a parallelogram are perpendicular, then the... (answered by Edwin McCravy)

Let's say you draw a kite and are instructed to do these things with it: 1. Construct... (answered by greenestamps)

Show that quadrilateral whose vertices are(-4,-2) (2,-10)(8,-5)(2,3) is a... (answered by jim_thompson5910)