Triangle Congruence SSS, SAS, ASA, AAS, 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 a 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 definition of triangle congruence?

Back

Triangle congruence means that two triangles are identical in shape and size, which can be proven using various postulates and theorems.

Front

Can two triangles be congruent if only one side is equal?

Back

No, two triangles cannot be congruent if only one side is equal; at least two sides and the included angle or other combinations must be equal.

Front

What is the significance of the included angle in SAS?

Back

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

Front

How can you prove two triangles are congruent using AAS?

Back

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

Front

What is an example of using SSS to prove congruence?

Back

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