Then, we also want ∠ACB and ∠ABC to be in different triangles, to prove their congruency. We know that ΔABC is isosceles, which means that AB=AC, so it will be good if we place these two sides in different triangles, and already have one congruent side. So let's think about a useful way to create two triangles here. Ok, but here we only have one triangle, and to use triangle congruency we need two triangles. This is the basic strategy we will try to use in any geometry problem that requires proving that two elements (angles, sides) are equal. If we can place the two things that we want to prove are the same in corresponding places of two triangles, and then we show that the triangles are congruent, then we have shown that the corresponding elements are congruent. Triangle congruency is a useful tool for the job. This problem is typical of the kind of geometry problems that use triangle congruency as the tool for proving properties of polygons. So how do we go about proving the base angles theorem? Prove that in isosceles triangle ΔABC, the base angles ∠ACB and ∠ABC are congruent. So, here's what we'd like to prove: in an isosceles triangle, not only are the sides equal, but the base angles equal as well. We will prove most of the properties of special triangles like isosceles triangles using triangle congruency because it is a useful tool for showing that two things - two angles or two sides - are congruent if they are corresponding elements of congruent triangles. In this lesson, we will show you how to easily prove the Base Angles Theorem: that the base angles of an isosceles triangle are congruent.
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