Question

Please help me thank you. show all work.

Answer 1

The length of OM is 4/3 the length of OJ, and the length of ON is 4/3 the length of OK. Thus, two pairs of sides from the triangles are proportional to each other.

Also, angle O from one of the triangles is equal to angle O of the other triangle because they are the same angle.

Thus, the two triangles are similar by SAS (side-angle-side) similarity theorem. This theorem is quite similar to the SAS congruence theorem.

To make a similarity statement, we just have to match corresponding parts when naming the triangle.

Similarity statement: ΔOJK~ΔOMN