Triangle Congruence (SSS, SAS, and 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 two 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 two 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 two triangles are congruent.

Front

What is the condition for two triangles to be congruent using SSS?

Back

Two triangles are congruent using SSS if all three corresponding sides are equal in length.

Front

What is the condition for two triangles to be congruent using SAS?

Back

Two triangles are congruent using SAS if 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 condition for two right triangles to be congruent using HL?

Back

Two right triangles are congruent using HL if their hypotenuses and one corresponding leg are equal.

Front

Can SSA (Side-Side-Angle) prove triangle congruence?

Back

No, SSA does not guarantee triangle congruence; it can lead to ambiguous cases.

Front

What is the significance of right angles in the HL theorem?

Back

In the HL theorem, both triangles must be right triangles, ensuring that the hypotenuse is opposite the right angle.

Front

Provide an example of SSS congruence. If triangle ABC has sides 5 cm, 7 cm, and 10 cm, what can be said about triangle DEF with sides 5 cm, 7 cm, and 10 cm?

Back

Triangle ABC is congruent to triangle DEF by SSS since all corresponding sides are equal.

Front

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

Back

If two triangles have two equal angles, the triangles are similar, but not necessarily congruent.