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 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 AAA criterion in triangle congruence?

Back

AAA stands for Angle-Angle-Angle, which states that if three angles of one triangle are equal to three angles of another triangle, the triangles are similar, but not necessarily congruent.

Front

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

Back

No, at least two sides and the included angle or specific combinations of sides and angles must be known to prove congruence.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is the angle between the two sides being compared; it is crucial for establishing congruence.

Front

How can you prove two triangles are congruent using SSS?

Back

To prove two triangles are congruent using SSS, show that all three corresponding sides of one triangle are equal to the three corresponding sides of the other triangle.

Front

What is the difference between AAS and ASA?

Back

AAS requires two angles and a non-included side, while ASA requires two angles and the included side.