Question

in a triangle ABC PQ is parallel to BC and BD is equal to DC prove that Pe is equal to EQ​

Answer 1

In △ABC, PQ∣∣BC and BD=DC.

We know that AD bisects PQ and PE=EQ

We also know that PE∣∣BD and EQ∣∣DC

But, it is given that BD=DC, therefore, PE∣∣EQ

(Because if two or more lines are parallel to the same line then they are parallel to each other)

Hence, PE∣∣EQ.

Answer 2

In Triangle ABC

• $\sf PQ || BC$
• $\sf BC = DC$

We Known that

• AD bisects PQ
• PE = EQ

We know also that

• PE || BC
• ED || DC

→ PE II EQ

(Because if two or more lines are parallel to the same line then they are parallel to each other)