SSS and SAS Triangle Congruence

Front

What does SSS stand for in triangle congruence?

Back

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

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem that states if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

What is the importance of order in triangle congruence?

Back

The order of the vertices matters in triangle congruence. For example, if ∆ABC ≅ ∆DEF, then angle A corresponds to angle D, angle B corresponds to angle E, and angle C corresponds to angle F.

Front

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

Back

No, knowing only one side is not enough to prove triangle congruence. You need at least two sides and the included angle (SAS) or all three sides (SSS).

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

If two triangles have two equal angles and one equal side, are they congruent?

Back

Yes, if two angles and the included side are equal (ASA), the triangles are congruent.

Front

What is the Angle-Side-Angle (ASA) theorem?

Back

The ASA theorem states that if two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the triangles are congruent.

Front

What is the Hypotenuse-Leg (HL) theorem?

Back

The HL theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

What is the difference between SSS and SAS?

Back

SSS requires all three sides to be equal, while SAS requires two sides and the included angle to be equal.

Front

What does it mean if two triangles are not enough information to prove congruence?

Back

It means that the given information does not provide sufficient data (like sides or angles) to determine if the triangles are congruent.