Question

Explain why the following triangles are similar to
each other.

Answer 1

The triangles are similar by AA similarity, with corresponding angles y, x, and z being equal. The sides are proportional, confirming the similarity.

The given triangles are similar based on the Angle-Angle (AA) similarity criterion. In both triangles, corresponding angles y, x, and z are equal. According to AA similarity, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

The corresponding sides are proportional as well. In triangle 1, the sides are given as 4n, 3n, and 7n. In triangle 2, the sides are given as 4, 7, and 3. To establish similarity, you can set up ratios for corresponding sides:

`\[ (4n)/(4) = (3n)/(3) = (7n)/(7) \]`

Solving these ratios, you find that n equals 1. Therefore, the sides of the triangles are indeed proportional.

In conclusion, with equal corresponding angles and proportional sides, triangle 1 is similar to triangle 2 based on the AA similarity criterion.