Lesson 4-6: Congruence in Overlapping Triangles

Front

What is congruence in triangles?

Back

Congruence in triangles means that two triangles are identical in shape and size, having corresponding sides and angles that are equal.

Front

What does the Reflexive Property state?

Back

The Reflexive Property states that any geometric figure is congruent to itself, meaning that for any triangle ABC, triangle ABC ≅ triangle ABC.

Front

What is the Angle-Angle-Side (AAS) Congruence Theorem?

Back

The AAS Congruence Theorem states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the Side-Angle-Side (SAS) Congruence Theorem?

Back

The SAS Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What is the Side-Side-Side (SSS) Congruence Theorem?

Back

The SSS Congruence Theorem states that if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Front

What is the significance of common angles or sides in overlapping triangles?

Back

Common angles or sides help establish congruence between overlapping triangles, allowing for the application of congruence theorems.

Front

What does it mean for angles to be congruent?

Back

Congruent angles are angles that have the same measure, regardless of their orientation or position.

Front

What is the definition of overlapping triangles?

Back

Overlapping triangles are triangles that share at least one vertex or side, allowing for the comparison of their properties.

Front

What is the Hypotenuse-Leg (HL) Theorem?

Back

The HL Theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

How do you identify common sides in overlapping triangles?

Back

Common sides can be identified by looking for sides that are shared between the two triangles, which can help in proving congruence.