Question

Parallelogram A B C D is shown. Line segment X Y goes from point X on side A B to point Y on side C D to form 2 trapezoids.

Figure ABCD is a parallelogram. Two trapezoids are created using line segment XY such that AX ≅ CY.

What is true about the areas of the trapezoids?

Each area is equal to half of the area of ABCD.
The area of AXYD is less than the area of BXYC.
The area of AXYD is greater than the area of BXYC.
Each area is equal to the area of ABCD.

Answer 1

A. ) Each area to equal to half of the area of ABCD

Explanation:

Edge 2021

Answer 2

Each area is equal to half the area of ABCD

Explanation:

AX ≅ CY

In parallelogram, opposite sides are equal.

AB = CD

AX + XB = CY + YD

CY + XB = CY + YD

XB = CY + YD - CY

XB = CY

Both trapezoids have equal area

Area of AXYD + area of BXYC = area of ABCD