Question

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Two similar triangles are shown below:

Two triangles are shown. The sides of the triangle on the left are marked 4, 5, 6. The sides of the triangle on the right are marked as 3, 2, and 2.5. For the triangle on the left, the angle between sides marked 6 and 5 is labeled as a, marked by a double arc, and the angle between the sides marked 6 and 4 is labeled as b, marked by a single arc. The third angle is marked by a triple arc. For the triangle on the right, the angle between sides marked 2 and 3 is labeled as c and the angle between the sides marked 2.5 and 3 is labeled as d, marked by a double arc. The angle between the sides 2 and 2.5 is labeled as e, marked by a triple arc, and it is also the angle on the top vertex of this triangle.
Which two sets of angles are corresponding angles? (4 points)

Group of answer choices

∠a and ∠e; ∠b and ∠c

∠a and ∠c; ∠b and ∠d

∠a and ∠e; ∠b and ∠d

∠a and ∠d; ∠b and ∠c

Answer 1

Explanation:

the 2 triangles are similar.

that means their corresponding angles are equal, and their side lengths (and heights and so on) have all the same constant scaling factor.

so, we see that the side with the length 6 must corresponds to the side with the length 3 (factor 1/2).

as then the side with the length 5 corresponds to the side with the length 2.5, and the side with the length 4 corresponds to the side with the length 2 (all have the same factor 1/2).

a is the angle between 6 and 5 (the 2 longest sides).

the angle between the 2 longest sides in the smaller triangle (3 and 2.5) is d.

so, a and d correspond.

b is the angle between 6 and 4 (the longest and the shortest side).

the angle between the corresponding sides 3 and 2 is c.

so, b and c correspond.

therefore, the 4th and last answer choice is correct.