Question

In triangle ABC, PQ is parallel to BC and BD is equal to DC .Prove that PE is equal to EQ.​

Answer 1

In Triangle ABC, PQ || BC and BD = DC.

We know that AD bisects PQ and PE = EQ

We also know that PE || BD and EQ II DC

But, it is given that BD = DC, therefore,

$\implies$PE II EQ

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

Hence, PE II EQ.

Answer 2

In Triangle ABC,

• PQ || BC
• BD = DC.

We know that

• AD bisects PQ
• PE = EQ

We also know that

• PE || BD
• EQ II DC

But, it is given that BD = DC, therefore,

$\longrightarrow$PE II EQ

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

Hence, PE II EQ.