Question

AD =BE

• A. True
• B. False

Answer 1

Answer: (A)

$\angle EPA=\angle DPB$(given)

$⟹\angle EPA+\angle DPE=\angle DPB+\angle DPE$

$\therefore \angle APD=\angle BPE$

Consider$△DAPand△EBP$

$AP=BP$ (given $P$ is midpoint of $AB$)

$\angle BAD=\angle ABE$ (given)

$\angle APD=\angle BPE$ (proved)

hence$△DAP\cong △EBP${ By ASA ccongruence rule\}

$⟹AD=BE\left\{CPCT\right\}$

$\therefore$ The statement is true.