Question

In an Isosceles Trapezoid ABCE with segment AB parallel to segment EC and segment AE parallel to segment AD, prove that ABCD is a:

A. Rectangle
B. Rhombus
C. Parallelogram
D. Kite

Answer 1

To prove that ABCD is a parallelogram, we need to show that opposite sides are parallel. In the given isosceles trapezoid ABCE, we know that AB is parallel to EC and AE is parallel to AD. Therefore, we have opposite sides AB and AD, as well as BC and EC, that are parallel. This satisfies the definition of a parallelogram.

Step-by-step explanation:

In order to prove that ABCD is a parallelogram, we need to show that opposite sides are parallel. In the given isosceles trapezoid ABCE, we know that AB is parallel to EC and AE is parallel to AD. Now, since AB is parallel to EC, and AE is parallel to AD, we can conclude that AB is also parallel to AD, and EC is parallel to BC (using the transitive property of parallel lines). Therefore, we have opposite sides AB and AD, as well as BC and EC, that are parallel. This satisfies the definition of a parallelogram.