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Given: NQ = NT , QS Bisect NT(∴ NS=ST ) , TV Bisects QN (∴ NV=VQ )
To Prove: QS=TV
Proof: In ΔNQT
NQ=NT
∴ VQ=ST
In a isosceles triangle, If two sides are equal then their opposites angles are equal.
∴ ∠NQT=∠NTQ ( ∵ NQ=NT)
In ΔQST and TVQ
ST=VQ (sides of isosceles triangle)
∠NQT=∠NTQ (Prove above)
QT=TQ (Common)
So, ΔQST ≅ TVQ by SAS congruence property
∴ QS=TV (CPCT)
CPCT: Congruent part of congruence triangles.
Hence Proved