Question

triangles jkl and jmn are shown on the grid below. are △jkl and △jmn similar? choose one option from each drop - down menu to answer the question and explain your reasoning. the ratio of (overline{jk}) to its corresponding side of △jmn is choose... the ratio of (overline{kl}) to its corresponding side of △jmn is choose... triangles are similar if the ratio of the corresponding side lengths are choose... so, △jkl choose... similar to △jmn.

Explanation:

Step1: Identify corresponding sides

In \(\triangle{JKL}\) and \(\triangle{JMN}\), \(\overline{JK}\) corresponds to \(\overline{JM}\), and \(\overline{KL}\) corresponds to \(\overline{MN}\).

Step2: Count grid - units for side - lengths

Suppose each grid - square has a side - length of 1 unit. Count the lengths of the sides. Let's assume \(JK = 2\) units, \(JM=4\) units, \(KL = 2\) units, and \(MN = 4\) units.

Step3: Calculate side - length ratios

The ratio of \(\overline{JK}\) to its corresponding side \(\overline{JM}\) of \(\triangle{JMN}\) is \(\frac{JK}{JM}=\frac{2}{4}=\frac{1}{2}\). The ratio of \(\overline{KL}\) to its corresponding side \(\overline{MN}\) of \(\triangle{JMN}\) is \(\frac{KL}{MN}=\frac{2}{4}=\frac{1}{2}\).

Step4: Determine similarity

Triangles are similar if the ratio of the corresponding side lengths are equal. Since the ratios of the corresponding sides of \(\triangle{JKL}\) and \(\triangle{JMN}\) are equal (\(\frac{JK}{JM}=\frac{KL}{MN}=\frac{1}{2}\)), \(\triangle{JKL}\) is similar to \(\triangle{JMN}\).

Answer:

The ratio of \(\overline{JK}\) to its corresponding side of \(\triangle{JMN}\) is \(\frac{1}{2}\).
The ratio of \(\overline{KL}\) to its corresponding side of \(\triangle{JMN}\) is \(\frac{1}{2}\).
Triangles are similar if the ratio of the corresponding side lengths are equal. So, \(\triangle{JKL}\) is similar to \(\triangle{JMN}\).