Equilateral triangle sides and angles congruent | Congruence | Geometry | Khan Academy

TL;DR

All three angles in an equilateral triangle have the same measure because the sides are congruent.

Transcript

What we've got over here is a triangle where all three sides have the same length, or all three sides are congruent to each other. And a triangle like this we call equilateral. This is an equilateral triangle. Now what I want to do is prove that if all three sides are the same, then we know that all three angles are going to have the same measure. ... Read More

Key Insights

• 🙃 An equilateral triangle has all three sides congruent to each other.
• 🔺 The base angles of an isosceles triangle with equal legs are congruent.
• 🔺 In an equilateral triangle, all three angles are congruent to each other.
• 🔺 The measure of each angle in an equilateral triangle is 60 degrees.
• 🔺 The congruence of base angles implies the congruence of sides in a triangle.
• 🔺 A triangle with congruent angles has congruent sides.
• 🔺 The sides and angles in an equilateral triangle are interdependent.

Questions & Answers

Q: What is an equilateral triangle?

An equilateral triangle is a triangle with all three sides of equal length.

Q: How can we prove that the angles in an equilateral triangle are congruent?

We can prove that the angles in an equilateral triangle are congruent by showing that the base angles of an isosceles triangle formed by its sides are congruent.

Q: What is the measure of each angle in an equilateral triangle?

Each angle in an equilateral triangle measures 60 degrees.

Q: Can we conclude that all sides are congruent if all angles in a triangle are congruent?

Yes, if all angles in a triangle are congruent, it can be concluded that all sides are congruent as well, as shown in the proof for an equilateral triangle.

Summary & Key Takeaways

• An equilateral triangle has all three sides congruent to each other.

• The base angles of an isosceles triangle with two equal sides are congruent.

• In an equilateral triangle, all three angles are congruent to each other.