# Geometry Basics Foundation

## Geometry Basics Foundation Revision

**Geometry Basics: The 5 Simple Rules**

**Geometry basics** will teach you the **5** simple rules needed to answer basic geometry questions, as well as give you the foundations to build as you work through the different geometry topics.

Having basic algebra knowledge is required to solve geometry problems.

**Angles in a triangle add up to 180\degree**

The angles in a triangle add up to 180\degree

\textcolor{red}{a} + \textcolor{skyblue}{b} + \textcolor{green}{c} = 180\degree

**Angles in a quadrilateral add up to 360\degree**

The angles in a quadrilateral (4 sided shape) add up to 360\degree

\textcolor{red}{a} + \textcolor{skyblue}{b} + \textcolor{green}{c} + \textcolor{yellow}{d}= 360\degree

**Angles on a straight line add up to 180\degree**

The angles on a straight line all add up to 180\degree

\textcolor{red}{a} + \textcolor{skyblue}{b} + \textcolor{green}{c} = 180\degree

**Angles around a point add up to 360\degree**

The angles around a point all add up to 360\degree

\textcolor{red}{a} + \textcolor{skyblue}{b} + \textcolor{green}{c} + \textcolor{yellow}{d}= 360\degree

**Two sides and two angles of an isosceles triangle are the same**

The two sides marked with the lines are the same length.

The two **base angles**, \textcolor{red}{x}, are the same.

**Example 1: Angles in a Triangle**

Find the value of x in the triangle shown:

**[2 marks] **

We know that angles in a triangle add up to 180\degree,

40\degree + 80\degree + x\degree = 180\degree

x= 180\degree -40\degree - 80\degree = 60\degree

x= 60\degree

**Example 2: Finding a Missing Angle**

Find the value of x in the triangle shown:

**[2 marks]**

We know that in an isosceles triangle, the base angles are equal.

This means we can form the equation:

x\degree + x\degree + 50\degree = 180\degree

2x\degree = 180\degree - 50\degree

2x = 130\degree

x\degree = 65\degree

## Geometry Basics Foundation Example Questions

**Question 1:** Given that the line ADB is a straight line, find the angle CDB shown below.

Give a reason for your answer.

**[2 marks] **

Angles on a straight line all add together to make 180\degree

\begin{aligned}103\degree+\angle CDB &= 180\degree \\ \angle CDB &= 180\degree-103\degree = 77\degree \end{aligned}

**Question 2:** A, B, C and D are points around a circle. Find the value of x.

**[2 marks] **

Angles around a point all add together to make 360\degree

100\degree+50\degree+x\degree+105\degree =360\degree \\ x=360\degree-100\degree-105\degree-50\degree \\ x= 105\degree

**Question 3:** DEF is an isosceles triangle. Find the value of y

Give a reason for your answer.

**[2 marks] **

Base angles in an isosceles triangle are equal and angles in a triangle add up to 180\degree

61\degree+61\degree+y\degree =180\degree \\ y\degree =180\degree-61\degree-61\degree \\ y=58\degree

**Question 4:** DEF is an isosceles triangle. Find the value of x

Give a reason for your answer.

**[2 marks] **

Base angles in an isosceles triangle are equal and angles in a triangle add up to 180\degree

\begin{aligned}x+x+55\degree&=180\degree \\ 2x&=180\degree-55\degree = 125\degree \\ x&=\dfrac{125\degree}{2}\end{aligned}

x=62.5\degree

**Question 5:** ACB forms a triangle shown below. ABD is a straight line.

Find the value of y

Give a reason for your answer.

**[3 marks] **

Angles on a straight line all add together to make 180\degree so

x=180\degree-115\degree=65\degree

Angles in a triangle add up to 180\degree

y=180\degree-25\degree-65\degree

y=90\degree