Congruent Triangles

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a postulate 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 AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a postulate 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 SSS postulate?

Back

SSS stands for Side-Side-Side, a postulate 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 ASA postulate?

Back

ASA stands for Angle-Side-Angle, a postulate 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 definition of a hypotenuse?

Back

The hypotenuse is the side opposite the right angle in a right triangle.

Front

If two triangles have two sides of equal length and the included angle is also equal, what can be concluded?

Back

The triangles are congruent by the SAS postulate.

Front

If two triangles have two angles of equal measure and a corresponding non-included side is equal, what can be concluded?

Back

The triangles are congruent by the AAS postulate.

Front

What is the relationship between congruent triangles?

Back

Congruent triangles have the same size and shape, meaning all corresponding sides and angles are equal.

Front

Solve for x: If triangle ABC is congruent to triangle DEF and AB = 5, DE = 5, BC = x, EF = 9, what is x?

Back

x = 9.

Front

What is the significance of triangle congruence in geometry?

Back

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