geom 8.2 flashcard

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

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 postulate?

Back

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

Front

What is the AAS theorem?

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 is the HL theorem?

Back

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

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

How can you prove triangles are congruent using SAS?

Back

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

Front

How can you prove triangles are congruent using ASA?

Back

To prove triangles are congruent using ASA, you need to show that two angles of one triangle are equal to two angles of another triangle, and the side between those angles is also equal.

Front

What is the relationship between SAS and ASA?

Back

SAS and ASA are both methods for proving triangle congruence, but SAS requires two sides and the included angle, while ASA requires two angles and the included side.

Front

What is the importance of triangle congruence theorems?

Back

Triangle congruence theorems are important because they provide a way to prove that two triangles are identical in shape and size, which is fundamental in geometry.