Question

What additional information must be known to prove the triangles similar by SAS?Question choices are in the image

Answer 1

Similar triangles are two or more triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

There are three rules for checking the similarity of two triangles:

1) Angle-Angle (AA) rule: This is when two angles of a triangle are equal to two angles of another triangle.

2) Side-Angle-Side (SAS) rule: This rule states that two triangles are similar if the ratio of their corresponding two sides is equal and also, the angle formed by the two sides is equal.

3) Side-Side-Side (SSS) rule: This rule is when the three sides of both triangles are in proportion.

The two triangles provided in the question are similar by the SAS rule. This means that they must have two corresponding sides in proportion and an equal angle formed by the two sides.

We have the following pair of sides and angles similar:

`\begin{gathered} |FG|\sim|KL| \\ \angle F\sim\angle K \end{gathered}`

To satisfy the SAS rule, the following pair of sides has to be provided:

`\begin{gathered} |DF| \\ \text{and} \\ |KJ| \end{gathered}`

Therefore, the correct option is OPTION B.