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

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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.

9th Grade Math

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