Question

In the given figure, AC = AE. Select the statements that are true.

• A. CP=EP
• B. BP= DP.
• C. 7BP= DP.
• D. CP=9EP

Answer 1

Answer: (A), (B)

The correct options are
A

CP=EP

B

BP= DP.

Given - In the figure, AC =AE

AC=AE (given)

$\angle ACD=\angle AEB$ (Angles in the same segment)

$\angle A=\angle A$ (Common)

$\Delta ADC\cong \Delta ABE$ (ASA postulate)

AB = AD (C.P.C.T.)

But AC = AE (given)

$\therefore AC-AB=AE-AD\Rightarrow BC=DE$

Now in $\Delta BPCand\Delta DPE$,

BC=DE (proved)

$\angle C=\angle E$ (Angles in the same segment)

$\angle CBP=\angle CDE$ (Angles in the same segment)

$\therefore \Delta BPC\cong \Delta DPE$ (S.A.S. postulate)

$\therefore$ BP= DP (C.P.C.T.)

CP= PE (C.P.C.T) Q.E.D.