Triangle Congruence Postulates

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 ASA stand for in triangle congruence?

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 does SSS stand for in triangle congruence?

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 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 does HL stand for 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, then the triangles are congruent.

Front

What is the SSA condition in triangle congruence?

Back

SSA stands for Side-Side-Angle, which does not guarantee triangle congruence. Two triangles can have two sides and a non-included angle equal but may not be congruent.

Front

How can you prove two triangles are congruent using the AAS postulate?

Back

To prove two triangles are congruent using AAS, you need to show that two angles and a non-included side of one triangle are equal to the corresponding two angles and the non-included side of the other triangle.

Front

What is the significance of the included angle in the SAS postulate?

Back

In the SAS postulate, the included angle is crucial because it is the angle formed between the two sides being compared, ensuring that the triangles are congruent.

Front

Can two triangles be congruent if they satisfy the SSA condition?

Back

No, two triangles satisfying the SSA condition are not necessarily congruent, as this condition can lead to ambiguous cases.

Front

What is the relationship between congruent triangles and their corresponding parts?

Back

If two triangles are congruent, then all their corresponding parts (sides and angles) are also congruent.