## How do you prove a 30 60 90 Triangle?

It is based on the fact that a 30°-60°-90° triangle is half of an equilateral triangle. Draw the straight line AD bisecting the angle at A into two 30° angles. Then AD is the perpendicular bisector of BC (Theorem 2). Triangle ABD therefore is a 30°-60°-90° triangle.

## What are the equivalent side ratios for a 30-60-90 Triangle?

This means that the ratio of the lengths of the shortest side to the hypotenuse of any right triangle is 1:2. Therefore, If a triangle is a right triangle, the ratio of the sides (short leg:long leg:hypotenuse) is 1:√3:2.

## How can you prove a right triangle?

Proof of Right Angle Triangle Theorem

1. Theorem:In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.
2. To prove: ∠B = 90°
3. Proof: We have a Δ ABC in which AC2 = AB2 + BC2
5. c2 = a2 + b2
6. c = √(a2 + b2)
7. A = 1/2 b x h.

## What are the lengths of a 45 45 90 Triangle?

A 45°-45°-90° triangle is a special right triangle that has two 45-degree angles and one 90-degree angle. The side lengths of this triangle are in the ratio of; Side 1: Side 2: Hypotenuse = n: n: n√2 = 1:1: √2. The 45°-45°-90° right triangle is half of a square.

3 units

## How do you find the missing side length of a 45 45 90 Triangle?

What are the lengths of the sides of a triangle? Using the pythagorean theorem – As a right angle triangle, the length of the sides of a triangle can easily be solved using the pythagorean theorem. Recall the pythagorean theorem formula: a 2 + b 2 = c 2 a^2+b^2=c^2 a2+b2=c2.

## Which is a true statement about a 45-45-90 Triangle?

In a triangle, the hypotenuse is times as long as one of the legs.

## Is a right triangle with two congruent legs always a 45 45 90 Triangle?

The given statement is true. A right triangle with two congruent legs is always a triangle.

## Which is a true statement about isosceles right triangle?

Isosceles Right Triangle Definition. An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent.

## What is the length of the hypotenuse of the triangle?

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

## What is the hypotenuse of a right triangle?

The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle.