Question

which of the following side lengths could not form a triangle congruent to one with sides 3 cm, 4 cm, and 5 cm by sss? a. 4 cm, 5 cm, 3 cm b. 4 cm, 3 cm, 5 cm c. 5 cm, 4 cm, 3 cm d. 3 cm, 4 cm, 6 cm if two triangles are congruent by sss, which of the following statements is true? a. only their side lengths are equal. b. they have the same area but different shapes. c. both their side lengths and corresponding angles are equal. d. only their angles are equal. which of the following conditions must be met to use the sss triangle congruence rule? a. two sides and the included angle must be equal. b. all three pairs of corresponding sides must be equal. c. two angles and the included side must be equal. d. all three pairs of corresponding angles must be equal.

Explanation:

Step1: Recall SSS congruence rule

The SSS (Side - Side - Side) congruence rule states that if all three pairs of corresponding sides of two triangles are equal, the triangles are congruent.

Step2: Analyze first question

For a triangle with sides 3 cm, 4 cm, and 5 cm, by SSS, any triangle with side - lengths 3 cm, 4 cm, 5 cm (in any order) is congruent. Option d has side - lengths 3 cm, 4 cm, 6 cm which cannot form a triangle congruent to the given one by SSS.

Step3: Analyze second question

If two triangles are congruent by SSS, then all three pairs of corresponding sides are equal. Also, by the SSS congruence, corresponding angles are equal (since the shape and size are identical). So both their side lengths and corresponding angles are equal.

Step4: Analyze third question

The condition for using the SSS triangle congruence rule is that all three pairs of corresponding sides must be equal.

Answer:

1. d. 3 cm, 4 cm, 6 cm
2. c. Both their side lengths and corresponding angles are equal.
3. b. All three pairs of corresponding sides must be equal.