We just showed that the three sides of △ D U C are congruent to △ D C K, which means you have the Side Side Side Postulate, which gives congruence. There! That's just D U C K y! Look at the two triangles formed by the median. We find P o i n t C on base U K and construct line segment D C: To mathematically prove this, we need to introduce a median line, a line constructed from an interior angle to the midpoint of the opposite side. The Isosceles Triangle Theorem states: If two sides of a triangle are congruent, then angles opposite those sides are congruent. Knowing the triangle's parts, here is the challenge: how do we prove that the base angles are congruent? That is the heart of the Isosceles Triangle Theorem, which is built as a conditional (if, then) statement: The two angles formed between base and legs, ∠ D U K and ∠ D K U, or ∠ D and ∠ K for short, are called base angles:.The third side is called the base (even when the triangle is not sitting on that side).

∠ D U ≅ ∠ D K, so we refer to those twins as legs.Like any triangle, △ D U K has three sides: D U, U K, and D K.Like any triangle, △ D U K has three interior angles: ∠ D, ∠ U, and ∠ K.What else have you got? Properties of an Isosceles Triangle If these two sides, called legs, are equal, then this is an isosceles triangle. Hash marks show sides ∠ D U ≅ ∠ D K, which is your tip-off that you have an isosceles triangle. You can draw one yourself, using △ D U K as a model. Here we have on display the majestic isosceles triangle, △ D U K.

No need to plug it in or recharge its batteries - it's right there, in your head! Yippee for them, but what do we know about their base angles? How do we know those are equal, too? We reach into our geometer's toolbox and take out the Isosceles Triangle Theorem. Isosceles triangles have equal legs (that's what the word 'isosceles' means). Isosceles Triangle Theorem (Proof, Converse, & Examples)

An isosceles triangle