Question

1. match.

the 45°-45°-90° triangle theorem states that in a 45°-45°-90° triangle, these legs are
dropdown and the length of the hypotenuse is
dropdown times the length of a leg.

a. √2
b. congruent
c. specific
d. √3

Explanation:

Step1: Analyze the first blank

In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the two legs are equal in length, which means they are congruent. So the first blank should be filled with "congruent" (option b).

Step2: Analyze the second blank

For a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, if the length of each leg is \(l\), using the Pythagorean theorem \(c^{2}=l^{2}+l^{2}=2l^{2}\), then the hypotenuse \(c = \sqrt{2l^{2}}=\sqrt{2}l\). So the length of the hypotenuse is \(\sqrt{2}\) times the length of a leg (option a).

Answer:

First blank: b. congruent; Second blank: a. \(\sqrt{2}\)