Question

If the 2 triangles are similar, write the similarity statement? how do you know?

Answer 1

The similarity statement is : ∆ 0MN is similar to ∆OJK by AA similarity. ( option A)

What are similar triangles?

Similar triangles have congruent angles and proportional side lengths.

Corresponding angles are equal, and the ratios of corresponding sides are constant.

For two triangles to be similar , the ratio of the corresponding sides must be equal and the corresponding angles are equal.

Angle O = angle O

Therefore,

40/4 = 30/3 = 10/1

Therefore, ∆ 0MN is similar to ∆OJK by AA similarity.

Answer 2

The triangles OMN and OJK are similar by SAS Similarity

How to Identify the Triangle Similarity Postulate?

The three triangle similarity theorems to prove triangles similar are:

Side-Angle-Side, or SAS.

Side-Side-Side, or SSS.

Angle-Angle, or AA.

Now, we are told that the triangles OMN and OJK are similar and as such, we this means that the ratio of their corresponding sides are in equal proportion.

Thus:

(30 + 10)/(3 + 1) = 40/4 = 10

Similarly, for the smaller triangle:

30/3 = 10

Thus, the ratios are equal.

We also see that Angle O is common to both triangles and as such:

The triangles OMN and OJK are similar by SAS Similarity