Congruent Triangles (SSS & SAS)

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a criterion for triangle congruence where all three sides of one triangle are equal to the three sides of another triangle.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

How can you determine if two triangles are congruent using SSS?

Back

If the lengths of all three sides of one triangle are equal to the lengths of all three sides of another triangle, then the triangles are congruent by SSS.

Front

How can you determine if two triangles are congruent using SAS?

Back

If two sides of one triangle are equal to two sides of another triangle and the angle between those sides is equal, then the triangles are congruent by SAS.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same shape and size, which means their corresponding sides and angles are equal, allowing for various applications in proofs and real-world problems.

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 relationship between congruent triangles and their corresponding angles?

Back

In congruent triangles, corresponding angles are also equal, which is a direct consequence of the congruence of the sides.

Front

If two triangles are not congruent, what can be said about their sides and angles?

Back

If two triangles are not congruent, at least one pair of corresponding sides or angles is different.

Front

Provide an example of a situation where SAS can be used to prove triangle congruence.

Back

If triangle ABC has sides AB = 5 cm, AC = 7 cm, and angle A = 60 degrees, and triangle DEF has sides DE = 5 cm, DF = 7 cm, and angle D = 60 degrees, then triangles ABC and DEF are congruent by SAS.

Front

Provide an example of a situation where SSS can be used to prove triangle congruence.

Back

If triangle GHI has sides GH = 8 cm, HI = 6 cm, GI = 10 cm, and triangle JKL has sides JK = 8 cm, KL = 6 cm, JL = 10 cm, then triangles GHI and JKL are congruent by SSS.