45-45-90 triangle
x, x, x√2
A 45-45-90 triangle, also known as an isosceles right triangle, is a triangle with two equal sides and one right angle (90 degrees). The two equal sides are opposite the two 45-degree angles.
Properties:
1. The length of the hypotenuse of a 45-45-90 triangle is equal to the length of one of the legs multiplied by the square root of 2 (√2).
2. The measure of each acute angle is 45 degrees.
3. The sum of the three angles in a triangle is always 180 degrees.
4. The legs of a 45-45-90 triangle are congruent.
Formulas:
1. The Pythagorean Theorem can be used to find the length of the hypotenuse of a 45-45-90 triangle: c = a√2, where c is the length of the hypotenuse and a is the length of one of the legs.
2. The area of a 45-45-90 triangle can be found using the formula A = 1/2 * leg^2.
Examples:
1. Given a 45-45-90 triangle with leg length of 4, what is the length of the hypotenuse?
Solution: Using the formula c = a√2, we get c = 4√2.
2. Given a 45-45-90 triangle with hypotenuse length of 10, what is the length of each leg?
Solution: Using the formula a = c/√2, we get a = 10/√2.
3. Given a 45-45-90 triangle with leg length of 3, what is the area of the triangle?
Solution: Using the formula A = 1/2 * leg^2, we get A = 4.5.
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