Equal Sides of an Isosceles Triangle are Produced, the Exterior Angles angles are equal.

Here we will prove if the equal sides of an isosceles triangle are produced, the exterior angles are equal.

Given: In the isosceles triangle PQR, the equal sides PQ and PR are produced to S and T respectively.

$Equal Sides of an Isosceles Triangle$

To prove: ∠RQS = ∠QRT.

Proof:

Statement

1. ∠PQR = ∠PRQ

2. ∠RQS = 180 – PQR.

3. ∠QRT = 180 - ∠PRQ

4. ∠QRT = 180 - ∠PQR

5. Therefore, ∠RQS = ∠QRT. (Proved)

Reason

1. Angles opposite to equal sides are equal.

2. Linear pair.

3. Linear pair.

4. Using statement 1.

5. Using statement 2 and 4.

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