# What is the theorem for a 45 45 90 triangle?

## What is the theorem for a 45 45 90 triangle?

What is the 45 45 90 triangle theorem? The 45 45 90 triangle theorem states that 45 45 90 special right triangles that have sides of which the lengths are in a special ratio of 1 : 1 : 2 1:1:\sqrt{2} 1:1:2 and two 45° angles and one right angle of 90°.

### What is the relationship between the legs and the hypotenuse of a 45-45-90 Triangle?

In other words, in every 45-45-90 triangle, the lengths of the two legs are always equal, and the ratio of the length of the hypotenuse to the length of a leg is always square root 2 to 1.

#### Which of the following is true in a 45 45 90 right triangle?

The 45°-45°-90° right triangle is half of a square. The diagonal of a square becomes hypotenuse of a right triangle, and the other two sides of a square become the two sides (base and opposite) of a right triangle.

What is the length of a 45 45 90 triangle?

In a 45°−45°−90° triangle, the length of the hypotenuse is √2 times the length of a leg. To see why this is so, note that by the Converse of the Pythagorean Theorem , these values make the triangle a right triangle.

What is a true statement about a 45 45 90 triangle apex?

Question: Which is a true statement about a 45-45-90 triangle? Each leg is times as long as the hypotenuse. The hypotenuse is times as long as either leg.

## What theorem will you use to find the length of the hypotenuse of a 45 45 90?

the Pythagorean Theorem
Correct answer: 45/45/90 triangles are always isosceles. This means that two of the legs of the triangle are congruent. In the figure, it’s indicates which two sides are congruent. From here, we can find the length of the hypotenuse through the Pythagorean Theorem.

### What is the theorem of the 45-45-90 triangle?

That tells us that for every 45-45-90 triangle, the length of the hypotenuse equals the length of the leg multiplied by square root of 2. That is the 45-45-90 Triangle Theorem.

#### Can a right triangle with a 45° angle be a 90° triangle?

A right triangle with two sides of equal lengths is a 45°-45°-90° triangle. You can also recognize a 45°-45°-90° triangle by the angles. As long as you know that one of the angles in the right-angle triangle is 45° then it must be a 45°-45°-90° special right triangle. A right triangle with a 45° angle must be a 45°-45°-90° special right triangle.

How to find the hypotenuse of a 45 / 45 / 90?

Find the length of the hypotenuse of the right triangle. 45/45/90 triangles are always isosceles. This means that two of the legs of the triangle are congruent. In the figure, it’s indicates which two sides are congruent. From here, we can find the length of the hypotenuse through the Pythagorean Theorem.

What kind of triangle has two sides equal to 45°?

A right triangle with two sides of equal lengths is a 45°-45°-90° triangle. You can also recognize a 45°-45°-90° triangle by the angles. As long as you know that one of the angles in the right-angle triangle is 45° then it must be a 45°-45°-90° special right triangle.