Triangle Congruency Theorems

Front

What does the SSS (Side-Side-Side) Congruence Theorem state?

Back

If three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What does the SAS (Side-Angle-Side) Congruence Theorem state?

Back

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

What does the ASA (Angle-Side-Angle) Congruence Theorem state?

Back

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 (Angle-Angle-Side) Congruence Theorem state?

Back

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 two triangles are congruent.

Front

What does the HL (Hypotenuse-Leg) Congruence Theorem state?

Back

In right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the two triangles are congruent.

Front

What is the difference between ASA and AAS?

Back

ASA requires the included side between two angles, while AAS does not require the side to be included between the two angles.

Front

Can SSA (Side-Side-Angle) be used to prove triangle congruence?

Back

No, SSA does not guarantee triangle congruence; it can lead to ambiguous cases.

Front

Provide an example of using the SAS theorem.

Back

If triangle ABC has AB = 5 cm, AC = 7 cm, and angle A = 60 degrees, and triangle DEF has DE = 5 cm, DF = 7 cm, and angle D = 60 degrees, then triangle ABC is congruent to triangle DEF by SAS.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which allows for the transfer of properties and measurements between them.

Front

How can you determine if two triangles are congruent using SSS?

Back

Measure all three sides of both triangles; if all three pairs of corresponding sides are equal, the triangles are congruent.