Triangle Congruencies: SSS,SAS,AAS,ASA,HL

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 theorem stating that 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, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a theorem applicable 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

What is the significance of triangle congruence theorems?

Back

Triangle congruence theorems are used to prove that two triangles are identical in shape and size, which is essential in solving geometric problems.

Front

Can SSA be used to prove triangle congruence?

Back

No, SSA (Side-Side-Angle) does not guarantee triangle congruence; it can lead to ambiguous cases.

Front

What is the difference between ASA and AAS?

Back

ASA requires the included side between two angles to be equal, while AAS allows for a non-included side to be equal.

Front

Provide an example of SSS in triangle congruence.

Back

If triangle ABC has sides of lengths 5, 7, and 9, and triangle DEF has sides of lengths 5, 7, and 9, then triangle ABC is congruent to triangle DEF by SSS.

Front

Provide an example of SAS in triangle congruence.

Back

If triangle XYZ has sides of lengths 6, 8 and an included angle of 60 degrees, and triangle PQR has sides of lengths 6, 8 and an included angle of 60 degrees, then triangle XYZ is congruent to triangle PQR by SAS.