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.
To prove: ∠RQS = ∠QRT.
1. ∠PQR = ∠PRQ
2. ∠RQS = 180 – PQR.
3. ∠QRT = 180 - ∠PRQ
4. ∠QRT = 180 - ∠PQR
5. Therefore, ∠RQS = ∠QRT. (Proved)
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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