Question

Given: bisects RTS R = S Prove: 1. Segment TQ bisects ∠RTS; ∠R = ∠S Definition of perpendicular. 2. ∠1 = ∠2 Definition of angle bisector. 3. TQ = TQ AAS 4. Triangle RTQ congruent to Triangle STQ Given 5. ∠3 = ∠4 CPCTE 6. Segment TQ ⊥ Segment RS Reflexive

Answer 1

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.