## Introduction

Unit 5 Relationships in Triangles is an important topic that students need to learn in order to understand the basics of geometry. This unit deals with the different relationships that exist between the sides and angles of a triangle. In this article, we will provide you with the answer key to this unit and guide you on how to understand and solve the different problems related to it.

## Angle Relationships

The first concept that you need to understand in this unit is the relationship between the angles of a triangle. There are three types of angles in a triangle: acute, right, and obtuse. An acute triangle has three angles that are less than 90 degrees, a right triangle has one angle that is exactly 90 degrees, and an obtuse triangle has one angle that is greater than 90 degrees.

One important relationship between the angles of a triangle is that the sum of the angles in a triangle is always 180 degrees. This means that if you know the measures of two of the angles in a triangle, you can easily find the measure of the third angle by subtracting the sum of the two known angles from 180 degrees.

## Side Relationships

The next concept that you need to understand in this unit is the relationship between the sides of a triangle. There are three types of triangles based on their sides: scalene, isosceles, and equilateral. A scalene triangle has all three sides of different lengths, an isosceles triangle has two sides of equal length, and an equilateral triangle has all three sides of equal length.

One important relationship between the sides of a triangle is the Pythagorean Theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.