Exercise 29 Page 396

We want to determine which of the given statements is always true. These statements are about the relationship between the measures of two acute angles of any right triangle. Let's start by looking at the two following right triangles.

In $△ABC,$ there are two acute angles with the same measure. In $△DEF,$ there are two acute angles with different measures. This means that a right triangle can have two equivalent acute angles or two scalene acute angles. Therefore, statements F and I are not always true. To analyze statements G and H, we will consider any right triangle.

Let's recall the Angle Sum of a Triangle Rule.

Angle Sum of a Triangle

The sum of the measures of the interior angles of a triangle is $180^{\circ }.$

With this rule, we can write an equation connecting the measures of the angles of any right triangle. Using this equation, we can find the sum of the measures of two acute angles of any right triangle. We got that the sum of two acute angles of any right triangle is $90^{\circ }.$ This means that these angles are complementary but not supplementary. Therefore, only statement G is always true about the relationship between the measures of two acute angles of any right triangle.