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.
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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