4.7 Congruent Postulates

Front

What does it mean for a line segment to be included between two angles?

Back

A line segment is included between two angles if it connects the vertices of the angles, forming a triangle.

Front

What does SSS stand for in triangle congruence?

Back

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

Front

What does SAS stand for in triangle congruence?

Back

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

Front

What does ASA stand for in triangle congruence?

Back

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

Front

What does AAS stand for in triangle congruence?

Back

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

Front

What is the HL postulate in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a postulate 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, the triangles are congruent.

Front

Can two triangles be congruent if only one side is known?

Back

No, at least two sides and the included angle or two angles and a side must be known to prove congruence.

Front

What is the significance of the included angle in triangle congruence?

Back

The included angle is crucial because it connects the two sides, and its measurement helps determine the triangle's shape and congruence.

Front

If two triangles have two equal angles, what can be concluded about their sides?

Back

If two triangles have two equal angles, their corresponding sides are proportional, but they may not be congruent unless the third side is also equal.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruent triangles are identical in shape and size, while similar triangles have the same shape but may differ in size.