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

A-Yes they have congruent corresponding angles

C-Yes they have proportional corresponding sides

Step-by-step 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.

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step-by-step explanation: