# Examples of triangle proofs

## What are the triangle proofs?

Triangle Sum Theorem: The three angles of a triangle sum to 180° Linear Pair Theorem: If two angles form a linear pair then they are adjacent and are supplementary. Third Angle Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent.

## What are 5 ways to prove a triangle?

**There are 5 main rules of congruency for triangles:**

- SSS Criterion: Side-Side-Side.
- SAS Criterion: Side-Angle-Side.
- ASA Criterion: Angle-Side- Angle.
- AAS Criterion: Angle-Angle-Side.
- RHS Criterion: Right angle- Hypotenuse-Side.

## What are the 3 types of proofs?

There are many different ways to go about proving something, we’ll discuss 3 methods:

**direct proof, proof by contradiction, proof by induction**. We’ll talk about what each of these proofs are, when and how they’re used.## Which theorem shows that △ ABC ≅ △ def?

By the

**SSS Congruence Theorem**, △ABC ≅ △DEF.## How do you write a triangle proof?

## What are the 4 ways to prove triangles are congruent?

**They are called SSS, SAS, and ASA.**

- SSS (Side-Side-Side) The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent. …
- SAS (Side-Angle-Side) …
- ASA (Angle-Side-Angle)

## How do you prove two triangles are similar?

**If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar**. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.

## Does SSA prove congruence?

**An SSA congruence theorem does exist.**

**can be used to prove triangles congruent**. sides and the corresponding nonincluded angle of the other, then the triangles are congruent. gruence if the angles indicated by the A are right or obtuse.

## How many ways can we prove Pythagorean Theorem?

This theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of each other sides square. There are many proofs which have been developed by a scientist, we have estimated

**up to 370**proofs of the Pythagorean Theorem.## How many ways can you prove Pythagoras theorem?

There are

**well over 371**Pythagorean Theorem proofs, originally collected and put into a book in 1927, which includes those by a 12-year-old Einstein (who uses the theorem two decades later for something about relatively), Leonardo da Vinci and President of the United States James A.## Can AAA prove triangles congruent?

**Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles**. When you’re trying to determine if two triangles are congruent, there are 4 shortcuts that will work.

## How do you prove triangle is 180 degrees?

**The angle sum of a triangle will always be equal to 180°**. The angle sum of a quadrilateral is equal to 360°, and a triangle can be created by slicing a quadrilateral in half from corner to corner. Since a triangle is essentially half of a quadrilateral, its angle measures should be half as well. Half of 360° is 180°.

## What is a Pythagorean triple give 3 examples?

Pythagorean theorem

Integer triples which satisfy this equation are Pythagorean triples. The most well known examples are **(3,4,5) and (5,12,13)**. Notice we can multiple the entries in a triple by any integer and get another triple. For example (6,8,10), (9,12,15) and (15,20,25).

## What are the 3 Pythagorean Theorem?

A Pythagorean triple consists of three positive integers a, b, and c, such that

**a**. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5).^{2}+ b^{2}= c^{2}## Who is the father of maths?

philosopher Archimedes

The Father of Math is

**the great Greek mathematician and philosopher Archimedes**. Perhaps you have heard the name before–the Archimedes’ Principle is widely studied in Physics and is named after the great philosopher.## Can 6 8 10 make a triangle?

**A triangle has sides of lengths 6, 8, and 10 is a right triangle**.

## What are the 4 most common Pythagorean triples?

The 5 most common Pythagorean triples are

**(3, 4, 5), (5, 12, 13), (6, 8, 10), (9, 12, 15), and (15, 20, 25)**.## Does 8 15 17 Form a right triangle?

**Yes, 8, 15, 17 is a Pythagorean Triple and sides of a right triangle**.

## Does 12/16 20 Make a right triangle?

The equation is true! So,

**a triangle with side lengths 12, 16, and 20 is a right triangle**.## What is the 3 4 5 Triangle rule?

The 3:4:5 triangle is the best way I know to determine with absolutely certainty that an angle is 90 degrees. This rule says that

**if one side of a triangle measures 3 and the adjacent side measures 4, then the diagonal between those two points must measure 5 in order for it to be a right triangle**.