8.1 and 8.2 Develop ASA and SAS triangle congruence

Kim draws a triangle with one 4 mm side, one 6 mm side, and a 25° included angle between those sides. If you follow the same steps as Kim to draw a triangle, is your triangle congruent to Kim’s triangle?

• Yes, the triangles are congruent based on SAS.

• No, the triangles are not congruent.

Two triangles have two pairs of congruent sides and a congruent pair of included angles. Can you map one triangle to the other?

• Yes, by using the SAS (Side-Angle-Side) Congruence Theorem.

• No, because the triangles are not congruent.

• Yes, but only if the triangles are right-angled.

• No, because the included angles are not congruent.

Explain the differences between the situations in which you would use the SAS Triangle Congruence Theorem versus the ASA Triangle Congruence Theorem.

• SAS is used when two sides and the included angle are known, while ASA is used when two angles and the included side are known.

• SAS is used when two angles and the included side are known, while ASA is used when two sides and the included angle are known.

• SAS is used when all three sides are known, while ASA is used when all three angles are known.

• SAS is used when two sides and a non-included angle are known, while ASA is used when two angles and a non-included side are known.

What must be true in order to use the ASA Triangle Congruence Theorem to prove that two triangles are congruent?

• If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

• If two side and the included angle of one triangle are congruent to two side and the included angle of another triangle, then the triangles are congruent.

QS is perpendicular to RP, and QS is an angle bisector of ∠PQR. Can you prove △PQS ≅ △RQS? Justify your answer.

• Yes, by Angle-Side-Angle (ASA) criterion

• Yes, by Side-Angle-Side (SAS) criterion

• No, they cannot be proven congruent

• Yes, by Hypotenuse-Leg (HL) criterion

Determine if the triangles are congruent, not congruent, or if there is not enough information to determine.

• Congruent
• Not Congruent

Determine if the triangles are congruent or not congruent.

• Congruent
• Not Congruent

Determine if the triangles are congruent or not congruent.

• Congruent

• Not Congruent

Two triangular road signs are mounted on the same post. They each have two pairs of 4-inch sides, and both have an included angle of 30°. Is it possible to prove the triangles are congruent?

• Yes, by SAS (Side-Angle-Side) congruence criterion.

• No, because the included angle is not sufficient to prove congruence.

• Yes, by SSS (Side-Side-Side) congruence criterion.

• No, because the triangles are not identical.

Which triangle congruence theorem can be used to prove the triangles are congruent?

• AAS
• SSS
• SAS
• SSA