Triangle Congruency Theorems

Front

What does AAS stand for in triangle congruency?

Back

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

Front

What is the SAS theorem?

Back

SAS stands for Side-Angle-Side, which states that 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

Define the SSS theorem.

Back

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

Front

What does HL stand for in triangle congruency?

Back

HL stands for Hypotenuse-Leg, a theorem applicable to right triangles that states 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 ASA theorem?

Back

ASA stands for Angle-Side-Angle, which states that 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 significance of the SSA condition in triangle congruency?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruency; it can lead to ambiguous cases where two different triangles can be formed.

Front

How can you prove triangles are congruent using the AAS theorem?

Back

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

Front

What is the relationship between the angles and sides in the SAS theorem?

Back

In the SAS theorem, the two sides must be adjacent to the included angle, which is the angle between the two sides.

Front

Can you explain the concept of congruency in triangles?

Back

Congruency in triangles means that two triangles are identical in shape and size, which can be proven using various congruency theorems.

Front

What is the criteria for using the SSS theorem?

Back

The SSS theorem can be used when all three sides of one triangle are known and can be compared to all three sides of another triangle.