Isosceles Triangle Properties

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About This Diagram

This visualization shows the Base Angles Theorem for isosceles triangles through three examples: parts identification, theorem application, and the converse.

Parts of an Isosceles Triangle

Part	Description
Legs	The two congruent sides
Base	The third side (not necessarily the bottom)
Vertex angle	The angle between the two legs
Base angles	The two angles at the ends of the base

Base Angles Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

In other words: Equal sides → Equal angles

Converse

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

In other words: Equal angles → Equal sides (triangle is isosceles)

Example Calculation

Given: AB = AC = 6 cm, ∠A = 40°

By Base Angles Theorem: ∠B = ∠C

Using Triangle Sum: 40° + 2∠B = 180°

Therefore: ∠B = ∠C = 70°

Interaction

Click anywhere to cycle through the three examples.

Learning Objectives

• Understand the relationship between equal sides and equal angles
• Apply the Base Angles Theorem to find unknown angles

Bloom's Taxonomy Level

Understanding and Applying

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