3 years ago

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Mathematics

1 answer:

blsea [12.9K]3 years ago

5 0

Given: NQ = NT , QS Bisect NT(∴ NS=ST ) , TV Bisects QN (∴ NV=VQ )

To Prove: QS=TV

Proof: In ΔNQT

NQ=NT

$\frac{1}{2}NQ=\frac{1}{2}NT$

∴ 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

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