EXTRA CREDIT: Triangle Congruence Check for Understanding

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem that states if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

List the five ways to prove triangles congruent.

Back

The five ways to prove triangles congruent are: SSS (Side-Side-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), SAS (Side-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem that states if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What is the SSS theorem?

Back

SSS stands for Side-Side-Side, a theorem that states if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

What is the HL theorem?

Back

HL stands for Hypotenuse-Leg, a theorem that states if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the SSA condition?

Back

SSA (Side-Side-Angle) is not a valid method for proving triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means their corresponding sides and angles are equal, allowing for various applications in proofs and real-world problems.

Front

How can you prove triangles are congruent using the SAS theorem?

Back

To prove triangles are congruent using SAS, show that two sides of one triangle are equal to two sides of another triangle and that the included angle between those sides is also equal.

Front

What is the difference between ASA and AAS?

Back

ASA requires the included side between two angles to be equal, while AAS allows for the non-included side to be equal, but both methods can prove triangle congruence.