Question

name
4 - 3 reteach to build understanding
proving and applying the sas and sss congruence criteria
envision geometry

1. are the triangles congruent? explain.

a. the two triangles are congruent by the _ triangle congruence theorem because two of their corresponding sides and the included angles are congruent.
b. the two triangles are congruent by the _ triangle congruence theorem because all three of their corresponding sides are congruent.

1. kiyo says that the triangles are congruent by the sas triangle congruence theorem. what is his error?
2. is \\( \triangle abc \cong \triangle def \\)? explain.

example
the triangles are congruent by sas.
b. the triangles _ congruent by _.
a. the triangles _ congruent by sas.
c. the triangles _ congruent by _.
envision™ geometry • teaching resources

Explanation:

Step1: Analyze problem 1a

The problem states that two corresponding sides and the included angles are congruent. This is the definition of the SAS (Side - Angle - Side) Triangle Congruence Theorem.

Step2: Analyze problem 1b

The problem states that all three corresponding sides are congruent. This is the definition of the SSS (Side - Side - Side) Triangle Congruence Theorem.

Step3: Analyze problem 2

For the SAS theorem, the angle must be included between the two sides. In the given triangles, the sides are not in the correct position relative to the angle for the SAS theorem to apply.

Step4: Analyze problem 3a

In the given triangles, the sides and angle do not match the SAS criteria (angle is not included between the corresponding sides).

Step5: Analyze problem 3b

The triangles are congruent by SSS as all three sides are marked as congruent.

Step6: Analyze problem 3c

The triangles are congruent by SSS as all three sides are marked as congruent.

Answer:

1. a. SAS; b. SSS
2. The angle is not the included angle between the two sides, so the SAS theorem does not apply.
3. a. are not; b. are, SSS; c. are, SSS