Triangle Congruence

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a criterion for triangle congruence where all three sides of one triangle are congruent to all three sides of another triangle.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle.

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 two triangles are congruent.

Front

If ∆ABC ≅ ∆XYZ, what can we conclude about the sides and angles?

Back

We can conclude that AB ≅ XY, BC ≅ YZ, AC ≅ XZ and ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z.

Front

What is the importance of triangle congruence in geometry?

Back

Triangle congruence is important because it allows us to determine that two triangles are identical in shape and size, which is fundamental in proving other geometric properties and theorems.

Front

How can you prove triangles are congruent using the SSS postulate?

Back

To prove triangles are congruent using the SSS postulate, show that all three sides of one triangle are equal in length to the corresponding sides of another triangle.

Front

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

Back

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

Front

What is the difference between ASA and AAS?

Back

ASA requires two angles and the included side to be congruent, while AAS requires two angles and a non-included side to be congruent.