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, which can be proven using various methods.

Front

Name the five ways to prove triangles congruent.

Back

SSS (Side-Side-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), SAS (Side-Angle-Side), HL (Hypotenuse-Leg for right triangles).

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a method of proving triangles congruent by showing that all three sides of one triangle are equal to the corresponding sides of another triangle.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a method of proving triangles congruent by showing that two angles and the included side of one triangle are equal to the corresponding parts of another triangle.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a method of proving triangles congruent by showing that two angles and a non-included side of one triangle are equal to the corresponding parts of another triangle.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a method of proving triangles congruent by showing that two sides and the included angle of one triangle are equal to the corresponding parts of another triangle.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a method of proving right triangles congruent by showing that the hypotenuse and one leg of one triangle are equal to the corresponding parts of another triangle.

Front

What is an overlapping triangle?

Back

An overlapping triangle is a triangle that shares one or more sides or angles with another triangle, allowing for the application of congruence principles.

Front

Identify a common angle in overlapping triangles.

Back

A common angle is an angle that is shared between two overlapping triangles, such as Angle D in triangles BDC and CEB.

Front

Identify a common side in overlapping triangles.

Back