1. Write as a simplified mixed number, improper fraction, or whole number.
1 answer:
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Solution:
Given : T Q bisects ∠RT S. And , ∠R=∠S
To Prove : T Q ⊥ R S
Proof : In Δ R T Q and Δ ST Q
T Q bisects ∠ R T S.
So, ∠1=∠2 →→→→ [Definition of angle bisector.]
T Q is Common.
∠R =∠S→→[Given]
Δ R T Q ≅ ST Q→→[AS A]
∵ ∠3 = ∠4 →→→ [C P C T E]
But ∠3 and ∠4 forms Linear pair.
∠3 + ∠4 = 180°
2 ∠3 = 180°
∠3 = 90°
∠3 = ∠4 =90°
So, Segment T Q ⊥ Segment RS .
Hence proved.
