Question

You know that a figure is a parallelogram. You use the distance formula to find the length of the diagonals. If they are both the same, what are the possibilities for what type of quadrilateral you have?

a) Rectangle
b) Trapezoid
c) Rhombus
d) Parallelogram

Answer 1

Answer: Rectangle (choice A)

Step-by-step explanation:

You can use the pythagorean theorem to prove the diagonals of any rectangle are congruent (aka the same length). Another approach is to use SAS before using CPCTC.

Some trapezoids have congruent diagonals, but that only applies to isosceles trapezoids. Furthermore, trapezoids aren't parallelograms, so we can rule out choice B for this reason.

A rhombus won't have congruent diagonals unless it's a square. Recall that any square is a rectangle, but not vice versa.

A non-rectangular parallelogram will never have congruent diagonals.