![]() ![]() Suppose a triangle ABC is an isosceles triangle, such that AB AC Two sides of the triangle are equal Hence, as per the theorem 2 B C. The angles opposite to equal sides of an isosceles triangle are also equal in measure. In today's lesson on proving the Converse Base Angle Theorem, we'll provide a proof for both. Theorem 2: The base angles of an isosceles triangle are congruent. Or, draw the angle bisector of A, and use the fact that it creates a pair of equal angles at A. We can draw either the altitude to the base, and use the fact that it creates a linear pair of equal right angles. And as a result, the corresponding sides, AB and AC, will be equal.Īnd just like in the original theorem, we have a choice of which line to draw. ![]() We'll do the same here, prove the triangles are congruent relying on the fact that the base angles are congruent. As a result, the base angles were congruent. There, we drew a line from A to the base BC and proved the resulting triangles are congruent. We will try to apply the same strategy we used to prove the original one - the Base Angles Theorem. When proving the Converse Base Angle theorem, we will do what we usually do with converse theorems. In triangle ΔABC, the angles ∠ACB and ∠ABC are congruent. Now we'll prove the converse theorem - if two angles in a triangle are congruent, the triangle is isosceles. As a consequence of that, the angles in the base are. We will use congruent triangles for the proof.įrom the definition of an isosceles triangle as one in which two sides are equal, we proved the Base Angles Theorem - the angles between the equal sides and the base are congruent. In particular, a triangle is said to be isosceles when at least two of their sides are congruent, that is, their lengths are the same. In today's lesson, we will prove the converse to the Base Angle theorem - if two angles of a triangle are congruent, the triangle is isosceles. ![]()
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