In triangle ABC, angle B is 36, AB = BC, AD is the bisector. Prove that triangle is ABD-isosceles.
September 16, 2021 | education
| 1. The sum of the angles of triangle ABC is 180 °:
∠A + ∠B + ∠C = 180 °, hence:
∠A + ∠C = 180 ° – ∠B;
∠A + ∠C = 180 ° – 36 ° = 144 °. (1)
2. In an isosceles triangle ABC, the angles at the base AC are:
∠A = ∠C;
From equation (1) we get:
∠A + ∠A = 144 °;
2∠A = 144 °;
∠A = 144 °: 2;
∠A = 72 °.
3. The bisector AD divides the angle A in half:
∠BAD = ∠CAD = 1/2 * ∠A = 1/2 * 72 ° = 36 °.
4. In triangle ABD, two angles are equal:
∠BAD = ∠B = 36 °,
therefore, it is isosceles, as required.
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