Contents

- 1 What properties or characteristics of similar triangles could be used to prove the Pythagorean Theorem?
- 2 How can we prove the Pythagorean Theorem?
- 3 How do you use the Pythagorean theorem to prove a right triangle?
- 4 Is the Pythagorean theorem true for all similar triangles?
- 5 How are similarity in right triangles and the Pythagorean theorem related?
- 6 What are the characteristics of similar triangles?
- 7 Is Pythagorean theorem wrong?
- 8 What type of triangle proves the Pythagorean Theorem?
- 9 What does the Pythagorean theorem allow us to do?
- 10 How do you prove if a triangle is a right triangle?
- 11 What is the longest side of a right triangle?
- 12 What are sides A and B called in Pythagorean Theorem?

## What properties or characteristics of similar triangles could be used to prove the Pythagorean Theorem?

Well, in order to prove the Pythagorean theorem, every triangle you are using has to have one right **angle** (90-degree **angle**), and the side opposite to it will be called the hypothenuse. The remaining two triangles will be acute **angles** (<90 degrees), and the sides opposite to them are called sides/catheti.

## How can we prove the Pythagorean Theorem?

**Pythagoras theorem** states that “In a right-angled triangle, the square of the hypotenuse side is equal **to** the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite **to** the angle 90°.

## How do you use the Pythagorean theorem to prove a right triangle?

The converse of the **Pythagorean Theorem** is: If the square of the length of the longest side of a **triangle** is equal to the sum of the squares of the other two sides, then the **triangle** is a **right triangle**.

## Is the Pythagorean theorem true for all similar triangles?

The **Pythagorean theorem** is **true for all** right **triangles**. It states that in right **triangle** the square of the hypotenuse which is the side opposite the right angle is equal to the sum of the squares of the other two sides. Therefore, the given statement is false. The **Pythagorean theorem** is **true for all** right **triangles**.

If the lengths of the hypotenuse and a leg of a **right triangle** are proportional to the corresponding parts of another **right triangle**, then the **triangles** are **similar**. (You can prove this by using the **Pythagorean Theorem** to show that the third pair of sides is also proportional.)

## What are the characteristics of similar triangles?

Two triangles are said to be similar if their corresponding angles are **congruent** and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same **size**. The triangles are **congruent** if, in addition to this, their corresponding sides are of equal **length**.

## Is Pythagorean theorem wrong?

Originally Answered: Is the **Pythagorean theorem false**? No. The **Pythagorean Theorem** remains true. The ancient Greeks thought about the **Pythagorean Theorem** as the quadrature of two squares.

## What type of triangle proves the Pythagorean Theorem?

The Pythagorean equation relates the **sides** of **a right triangle** in a simple way, so that if the **lengths** of any two **sides** are known the **length** of the third **side** can be found. Another corollary of the theorem is that in any **right triangle**, the **hypotenuse** is greater than any one of the other **sides**, but less than their **sum**.

## What does the Pythagorean theorem allow us to do?

The **Pythagoras theorem** is a mathematical law that states that the sum of squares of the lengths of the two short sides of the right triangle is equal to the square of the length of the hypotenuse.

## How do you prove if a triangle is a right triangle?

A **triangle** can be determined to be a **right triangle if** the side lengths are known. **If** the lengths satisfy the Pythagorean Theorem (a2+b2=c2) then it is a **right triangle**.

## What is the longest side 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. The other two sides are called the opposite and adjacent sides.

## What are sides A and B called in Pythagorean Theorem?

The Pythagorean theorem consists of a formula a^2+b^2=c^2 which is used to figure out the value of (mostly) the hypotenuse in a right **triangle**. The a and b are the 2 “non-hypotenuse” sides of the **triangle** (Opposite and Adjacent).