Question

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

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.
a. the triangles _ congruent by sas.
b. the triangles _ congruent by _.
c. the triangles _ congruent by _.

Explanation:

Step1: Analyze problem 1a

The Side - Angle - Side (SAS) Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In problem 1a, two sides and the included angle are congruent, so the blank is filled with "SAS".

Step2: Analyze problem 1b

The Side - Side - Side (SSS) Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In problem 1b, all three corresponding sides are congruent, so the blank is filled with "SSS".

Step3: Analyze problem 2

For the SAS Congruence Theorem, the angle must be the included angle between the two sides. In the given triangles for problem 2, the angle is not the included angle between the two marked sides. So Kiyo's error is that the angle is not the included angle for the two sides he is considering for the SAS theorem.

Step4: Analyze problem 3a

For the triangles in problem 3a, the sides and angle do not match the SAS criteria (the angle is not in the correct position relative to the sides). So the answer is "are not".

Step5: Analyze problem 3b

Looking at the triangles in the example for 3b, the sides and angle match the SAS criteria. So the answer is "are" and "SAS".

Step6: Analyze problem 3c

For the triangles in 3c, all three sides match the SSS criteria. So the answer is "are" and "SSS".

Answer:

1. a. SAS; b. SSS
2. Kiyo's error is that the angle is not the included angle for the two sides he is using for the SAS theorem.
3. a. are not; b. are, SAS; c. are, SSS