Question

1. choose the best answer.

a 45°- 45°-90° right triangle is also called an ______ right triangle.
iscosceles
acute

1. choose the best answer.

apply the 45°-45°-90° triangle theorem to find the length of the hypotenuse of a right triangle with the length of leg a 5 inches.
25 inches
2√5 inches
10 inches
5√2 inches

Explanation:

Question 3

In a \(45^\circ - 45^\circ - 90^\circ\) right triangle, two angles are equal (\(45^\circ\) each). By the property of triangles, sides opposite equal angles are equal. An isosceles triangle has at least two equal sides (and thus two equal angles). An acute triangle has all angles less than \(90^\circ\), but this triangle has a \(90^\circ\) angle, so it's a right triangle, not just acute. So the \(45^\circ - 45^\circ - 90^\circ\) triangle is isosceles.

Step1: Recall the \(45^\circ - 45^\circ - 90^\circ\) Triangle Theorem

In a \(45^\circ - 45^\circ - 90^\circ\) right triangle, the length of the hypotenuse \(c\) is related to the length of each leg \(a\) (since the two legs are equal) by the formula \(c = a\sqrt{2}\).

Step2: Substitute the given leg length

Given that the length of leg \(a = 5\) inches. Substitute \(a = 5\) into the formula \(c = a\sqrt{2}\). So \(c = 5\sqrt{2}\) inches.

Answer:

A. isosceles

Question 4