Question

PQ is the bisector of ∟LPK and PK=PL. Are the triangles PKQ and PLQ equal? Prove
that QK=QL.

Answer 1

Given :-

• PQ is the angle is the angle bisector of LPK
• PK = PL

To prove :-

• QK = QL

Solution :-

→ In ∆ PLQ & ∆PKQ

1. PK = PL [given]
2. angle LPQ = angle KPQ [ Since PQ is the angle bisector]
3. PQ = PQ [common in both ∆s]

So, ∆PLQ congruent to ∆PKQ (BY SAS congruency)

ans 1. = YES THEY ARE EQUAL !

=> QK = QL (BY CPCT)

HOPE IT HELPS YOU ! ✨