Question

1. △lmn and △jkn

Explanation:

Step1: Identify Similar Triangles

Assume we need to check similarity or find a missing side. First, check angles: $\angle LNM = \angle JNK$ (vertical angles), and $\angle K = \angle M = 90^\circ$ (right angles), so $\triangle LMN \sim \triangle JKN$ by AA similarity.

Step2: Set Up Proportion

Let’s find the ratio of corresponding sides. For $\triangle JKN$ and $\triangle LMN$: $\frac{JN}{LN} = \frac{3.6}{18} = 0.2$, $\frac{KN}{MN} = \frac{3}{15} = 0.2$. Ratios are equal, confirming similarity.

(If finding a missing side, say $LM$: Let $LM = x$. Then $\frac{JK}{LM} = \frac{3.6}{x} = \frac{3}{15} \implies 3x = 3.6 \times 15 \implies x = 18$.)

Answer:

The triangles are similar by AA similarity (or missing side calculation gives $LM = 18$ if needed).