Triangle Congruency Shortcuts (SSS SAS AAS ASA HL)

Front

What does SSS stand for in triangle congruency?

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 congruency?

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 AAS stand for in triangle congruency?

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 ASA stand for in triangle congruency?

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 corresponding included side of another triangle, the triangles are congruent.

Front

What does HL stand for in triangle congruency?

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

Which triangle congruency shortcut is NOT valid?

Back

SSA (Side-Side-Angle) is not a valid shortcut for proving triangle congruency.

Front

If ∠A ≅ ∠D, what can be inferred about the triangles?

Back

If ∠A ≅ ∠D, it indicates that the triangles may be congruent, but additional information about sides or other angles is needed to confirm congruency.

Front

Are the triangles congruent if two angles and a side are known?

Back

Yes, if two angles and a side are known, the triangles can be proven congruent using the AAS or ASA postulates.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is crucial because it must be between the two sides being compared for the triangles to be congruent.

Front

Can two triangles be congruent if only two sides are known?

Back

Not necessarily; knowing only two sides (SS) does not guarantee congruency without additional information about angles.