If a triangle has two congruent angles, then…
it is an isosceles triangle
If a triangle has two congruent angles, then it must be an isosceles triangle. This is because in any triangle, the sum of the three interior angles is always 180 degrees. When two angles in a triangle are congruent, we can call them base angles, as they are opposite the two equal sides of the triangle. Therefore, the sum of the base angles in an isosceles triangle is 180 minus the third angle. Since the two base angles are congruent (equal), we can find each angle by dividing that difference by 2.
For example, if we have a triangle with two congruent angles of 70 degrees each, then the third angle can be found by subtraction of 140 from 180 (180 – 140 = 40 degrees). We can divide this value by 2 to find each of the base angles, which would be 20 degrees each. Thus, we have determined that the third angle is 40 degrees and the base angles are each 20 degrees. In this way, we have shown that the triangle is indeed an isosceles triangle.
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