![]() ![]() In today's lesson on proving the Converse Base Angle Theorem, we'll provide a proof for both. 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. These two congruent sides are called the legs of the triangle. By definition, a triangle that has two congruent sides is an isosceles triangle. As a result, the base angles were congruent. Answer In this triangle, we can observe that there are two sides of equal length: the lengths of and are both given as 2 cm. 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. 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 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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