Question

which similarity statement describes the relationship between a triangle with angles m∠A = 48, m∠B = 17 and m∠C = 115 and another triangle with angles m∠H = 17, m∠I = 48, and m∠J = 115
Answers:
A. △CAB ~ △JHI
B. △ABC ~ △HIJ
C. △BAC ~ △HIJ
D. △BCA ~ △JIH

Answer 1

To determine the similarity statement between the two triangles, we first note the angles of each triangle.

For triangle ABC:
- m∠A = 48°
- m∠B = 17°
- m∠C = 115°

For triangle HIJ:
- m∠H = 17°
- m∠I = 48°
- m∠J = 115°

Now we can arrange the angles in order from the smallest to the largest for clarity.

For triangle ABC:
- m∠B = 17° (smallest)
- m∠A = 48°
- m∠C = 115° (largest)

For triangle HIJ:
- m∠H = 17° (smallest)
- m∠I = 48°
- m∠J = 115° (largest)

Now we can see that the angles correspond as follows:
- m∠B (17°) corresponds to m∠H (17°)
- m∠A (48°) corresponds to m∠I (48°)
- m∠C (115°) corresponds to m∠J (115°)

Thus, the triangles have the same angles, and we can state that the triangles are similar by AA (Angle-Angle) similarity.

The correct similarity statement based on the matching angles is:
**B. △ABC ~ △HIJ**

This indicates that triangle ABC is similar to triangle HIJ.