Triangle Congruency

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem stating that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem stating 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 triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem stating 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 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, then 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, then 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 congruent, meaning they have the same size and shape, which is essential in solving geometric problems.

Front

List the five main ways to prove triangles congruent.

Back

The five main ways to prove triangles congruent are SSS, SAS, ASA, AAS, and HL.

Front

If ∆ABC ≅ ∆DEF, what can be concluded about the angles?

Back

If ∆ABC ≅ ∆DEF, then ∠A ≅ ∠D, ∠B ≅ ∠E, and ∠C ≅ ∠F.

Front

If two triangles have two pairs of equal angles, what can be said about the triangles?

Back

If two triangles have two pairs of equal angles, they are congruent by the AAS theorem.

Front

Can SSA be used to prove triangle congruence? Why or why not?

Back

SSA (Side-Side-Angle) cannot be used to prove triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.