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Geometry Basics Foundation Worksheets, Questions and Revision

Level 1-3
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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. 

Level 1-3

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

Level 1-3

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

Level 1-3

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

Level 1-3

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

Level 1-3

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. 

Level 1-3
Level 1-3

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

Level 1-3

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

Level 1-3
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Example Questions

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}

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

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

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

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

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