Question

In the diagram below, if < A = 111 °, < B = 52 °, < D =111 ° and < F = 17 °, we can say that ___.

Answer 1

Given: Triangles ABC and DEF are given such that

`\begin{gathered} \angle A=111\degree \\ \angle B=52\degree \\ \angle D=111\degree \\ \angle F=17\degree \end{gathered}`

Required: To determine the similarity of the given triangles.

Explanation: Two triangles are said to be similar if their corresponding angles are equal.

In triangle ABC, we have-

`\angle A+\angle B+\angle C=180\degree\text{ ...}(\text{Angle sum property})`

Thus,

`\begin{gathered} \angle C=180\degree-111\degree-52\degree \\ \angle C=17\degree \end{gathered}`

Now, in triangles ABC and DEF, we have

`\begin{gathered} \angle A=\angle D \\ \angle C=\angle F \end{gathered}`

Therefore, by the AA rule of similarity

Final Answer: Option C is correct.