Question

Daniela examines the two triangles below and determines DAC~TRS.

Which best describes the accuracy of Daniela’s solution?
A. Accurate. The triangles are similar and the congruent angles are listed in corresponding order.
B. Inaccurate. In her statement, the corresponding vertices are written in the incorrect order.
C. Inaccurate. There is only one pair of congruent angles, so no statement can be made on the similarity of the triangles.
D. Inaccurate. The triangles are not similar because angle D is not congruent to angle R.

Answer 1

A

Explanation:

Answer 2

Option A. Accurate. The triangles are similar and the congruent angles are listed in corresponding order

Explanation:

step 1

In the triangle TRS find the measure of angle T

Remember that

The sum of the interior angles in a triangle is equal 180 degrees

so

`<T+<R+<S=180\°`

substitute the values and solve for <T

`<T+55.1\°+67\°=180\°`

`<T=180\°-(55.1\°+67\°)=57.9\°`

so

The triangle DAC is similar to triangle TRS by AA Similarity Postulate (The three interior angles are congruent)

The corresponding angles are

<S=<C

<R=<A

<T=<D

therefore

The triangles are similar and the congruent angles are listed in corresponding order DAC~TRS