Congruent legs and base angles of isosceles triangles | Congruence | Geometry | Khan Academy

TL;DR

Isosceles triangles have two congruent sides and two congruent base angles, and their congruency can be proven using triangle congruency theorems.

Transcript

So we're starting off with triangle ABC here. And we see from the drawing that we already know that the length of AB is equal to the length of AC, or line segment AB is congruent to line segment AC. And since this is a triangle and two sides of this triangle are congruent, or they have the same length, we can say that this is an isosceles triangle.... Read More

Key Insights

• 🔺 Isosceles triangles have two congruent sides and two congruent base angles.
• 🔺 Congruent triangles can be constructed from an isosceles triangle using triangle congruency theorems.
• 🔺 The congruency of base angles in an isosceles triangle can be proven by constructing congruent triangles with a midpoint.
• 🔺 The congruency of legs in an isosceles triangle can be proven by constructing congruent triangles using an altitude.
• ⚾ Point D in an isosceles triangle can be both the midpoint of the base and where the perpendicular bisector of the base intersects.

Questions & Answers

Q: What defines an isosceles triangle?

An isosceles triangle is a triangle that has two congruent sides and two congruent base angles.

Q: How can you prove that the base angles of an isosceles triangle are congruent?

By constructing congruent triangles with a midpoint or an altitude, you can prove that the base angles of an isosceles triangle are congruent.

Q: Can you prove that the legs of an isosceles triangle are congruent if the base angles are congruent?

Yes, by constructing congruent triangles using an altitude, you can prove that the legs of an isosceles triangle are congruent if the base angles are congruent.

Q: Is it possible for an isosceles triangle to have more than two congruent angles?

No, an isosceles triangle can only have two congruent angles, the base angles, while the vertex angle is always different from the other two angles.

Summary & Key Takeaways

• An isosceles triangle has two congruent sides and two congruent base angles.

• The congruency of the base angles in an isosceles triangle can be proven by constructing two congruent triangles using a midpoint or an altitude.

• The congruency of the legs in an isosceles triangle can also be proven by constructing congruent triangles using an altitude.