Table of Contents

## What are the characteristics of vector addition?

Addition of vectors satisfies two important properties.

- The commutative law, which states the order of addition doesn’t matter: a+b=b+a.
- The associative law, which states that the sum of three vectors does not depend on which pair of vectors is added first: (a+b)+c=a+(b+c).

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

Classifying Triangles by Using the Pythagorean Theorem If you plug in 5 for each number in the Pythagorean Theorem we get 52+52=52 and 50>25. Therefore, if a2+b2>c2, then lengths a, b, and c make up an acute triangle. Conversely, if a2+b2triangle.

**What are the properties of a 45 45 90 Triangle?**

45−45−90 refers to the angles of the triangle. There are two equal angles , so this is an isosceles triangle. It therefore also has two equal sides. The third angle is 90° .

### How do you prove a 45 45 90 Triangle?

Using the pythagorean theorem – As a right angle triangle, the length of the sides of a 45 45 90 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.

### How do you find the area of a 45 45 90 Triangle?

To find the area of a triangle, multiply the base by the height, then divide by 2. Since the short legs of an isosceles triangle are the same length, we need to know only one to know the other. Since, a short side serves as the base of the triangle, the other short side tells us the height.

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

In a 45-45-90 triangle, both of the legs have the same length and the ratio of one leg to the hypotenuse is 1:sqrt(2). I hope this helps!

#### Is an isosceles right triangle always a 45 45 90 Triangle?

As these two angles are equal (the triangle being isoceles), each of the angle is 90o2=45o . Hence, an isosceles right triangle always a 45o−45o−90o triangle.