Proving Congruent Triangles- SSS, SAS, HL

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 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 CPCTC?

Back

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent, a principle used to prove that corresponding sides and angles of congruent triangles are equal.

Front

If ∆ABC ≅ ∆XYZ, what can be concluded about side AB?

Back

AB ≅ XY, meaning side AB of triangle ABC is congruent to side XY of triangle XYZ.

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 must be equal (SAS) or all three sides must be equal (SSS).

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself, meaning for any triangle ∆ABC, ∆ABC ≅ ∆ABC.

Front

How can you prove triangles are congruent using the SAS theorem?

Back

To prove triangles are congruent using SAS, show that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

What is the difference between ASA and AAS in triangle congruence?

Back

ASA stands for Angle-Side-Angle, while AAS stands for Angle-Angle-Side. Both can be used to prove triangle congruence, but ASA requires the included side, while AAS does not.

Front

If two triangles have two angles equal, what can be said about their sides?

Back

If two triangles have two angles equal, the third angle is also equal, and the triangles are similar, but not necessarily congruent unless a side is also equal.