Triangle Congruence Theorems

Front

What does the HL Congruence Theorem state?

Back

The HL (Hypotenuse-Leg) Congruence Theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

Define the SSS Congruence Theorem.

Back

The SSS (Side-Side-Side) Congruence Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What is the SAS Congruence Theorem?

Back

The SAS (Side-Angle-Side) Congruence Theorem 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 two triangles are congruent.

Front

Explain the ASA Congruence Theorem.

Back

The ASA (Angle-Side-Angle) Congruence Theorem 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 two triangles are congruent.

Front

What does the AAS Congruence Theorem state?

Back

The AAS (Angle-Angle-Side) Congruence Theorem states 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, then the two triangles are congruent.

Front

What is the SSA condition in triangle congruence?

Back

The SSA (Side-Side-Angle) condition does not guarantee triangle congruence, as it can lead to ambiguous cases where two different triangles can be formed.

Front

What is the significance of the term 'congruent' in geometry?

Back

In geometry, 'congruent' means that two figures have the same shape and size, allowing them to be superimposed on each other.

Front

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

Back

To prove triangles are congruent using the SSS theorem, measure all three sides of both triangles and show that they are equal.

Front

What is the difference between ASA and AAS?

Back

ASA requires two angles and the included side to be equal, while AAS requires two angles and a non-included side to be equal for triangle congruence.

Front

Can two triangles be congruent if only one angle and two sides are known?

Back

No, knowing only one angle and two sides (SSA) does not guarantee triangle congruence due to the possibility of multiple configurations.