Question

Are the two triangles below similar?

A-Yes they have congruent corresponding angles
B-No they don't have congruent corresponding angles
C-Yes they have proportional corresponding sides
D-No they don't have proportional corresponding sided

Answer 1

I think the answer is B but I'm not sure

Answer 2

A-Yes they have congruent corresponding angles

C-Yes they have proportional corresponding sides

Explanation:

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

The measure in the angle B is: 180° - 38° - 84° = 58° = angle E

The measure in the angle D is: 180° - 38° - 58° = 84° = angle A

So their corresponding angles are congruent .

From law of sine:

12/sin(84°) = BA/sin(38°)

[12/sin(84°)]*sin(38°) = BA

7.65 ≈ BA

12/sin(84°) = AC/sin(58°)

[12/sin(84°)]*sin(58°) = AC

10.2 ≈ AC

8/sin(58°) = EF/sin(84°)

8/sin(58°)*sin(84°) = EF

9.41 ≈ EF

The next proportion is also satisfied 12/9.41 = 7.65/6 = 10.2/8 = 1.275. Then, the corresponding sides are in proportion.