Question

If the diagonals of a parallelogram are congruent then what would be the best and

most restrictive description of that quadrilateral?
a) Kite
b) Rectangle
c) Trapezoid
d) Rhombus

Answer 1

Answer: b) Rectangle.

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Step-by-step explanation:

If the diagonals were congruent, then you can use the SSS property to prove a pair of right triangles are congruent. This leads to showing that we have adjacent congruent corresponding angles. Let's call those angles x and y.

Since they are congruent, we know that y = x. Adjacent angles of any parallelogram add to 180, so x+y = 180

By substitution we can solve for x

x+y = 180

x+x = 180

2x = 180

x = 180/2

x = 90

So y = 90 as well.

This line of thinking is used to show that all four angles of this parallelogram are 90 degrees. A rectangle is any quadrilateral in which all four angles are 90 degrees, so that's why this parallelogram is a rectangle.