Question

1. if two triangles are congruent by sss, what can be inferred about their perimeters? a. their perimeters depend on the triangles orientation. b. their perimeters will be equal. c. their perimeters will be different. d. their perimeters depend on the angles. 8. which of the following triangles are congruent to triangle abc with sides 4 cm, 5 cm, 6 cm? a. mno with sides 5 cm, 6 cm, 7 cm b. def with sides 4 cm, 5 cm, 7 cm c. jkl with sides 3 cm, 4 cm, 5 cm d. ghi with sides 4 cm, 5 cm, 6 cm 9. which of the following statements is true if two triangles are congruent by asa? a. they have corresponding angles and included side that are equal b. they have the same angles, but their side lengths differ c. they are similar, but not congruent d. they have the same area but different perimeters

Explanation:

Step1: Recall SSS congruence property

If two triangles are congruent by SSS (Side - Side - Side), their corresponding sides are equal. The perimeter of a triangle is the sum of its side - lengths. Since corresponding sides are equal, perimeters are equal. So for question 7, the answer is b.

Step2: Apply SSS congruence for triangle comparison

For two triangles to be congruent by SSS, all three pairs of corresponding sides must be equal. Triangle ABC has sides 4 cm, 5 cm, 6 cm. Among the options for question 8, only triangle GHI with sides 4 cm, 5 cm, 6 cm has the same side - lengths, so the answer is d.

Step3: Recall ASA congruence property

If two triangles are congruent by ASA (Angle - Side - Angle), it means they have two corresponding angles and the included side equal. For question 9, option a is correct.

Answer:

1. b. Their perimeters will be equal.
2. d. GHI with sides 4 cm, 5 cm, 6 cm
3. a. They have corresponding angles and included side that are equal