Question

If ABCD is a parallelogram and BEFC is a square which of the following is true?

• A. True
• B. False
• C. $\angle ABE=\angle DCF$
• D. $EF=AD$

Answer 1

Answer: (A), (C), (D)

The correct options are
A

True

C

$\angle ABE=\angle DCF$

D

$EF=AD$

Given: ABCD is a parallelogram and BEFC is a square.

Consider $△ABE$ and $△DCF$

AB = DC [Opposite sides of a parallogram]

BE = CF [Sides of a square]

$\angle ABE=\angle DCF$ [By geometry]

$\therefore △ABE\cong △DCF$ [SAS axiom on congruency]

EF = BC [Sides of a square]

BC = AD [Opposite sides of a parallelogram]

Therefore EF = AD