Geometry Problems Worksheets | Questions and Revision | MME

Geometry Basics Foundation Worksheets, Questions and Revision

Level 1-3

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

angles in a triangle 180 degrees

The angles in a triangle add up to 180\degree

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

angles in a triangle 180 degrees
Level 1-3

Angles in a quadrilateral add up to 360\degree

angles in a quadrilateral 360 degrees

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 in a quadrilateral 360 degrees
Level 1-3

Angles on a straight line add up to 180\degree

Angles on a straight line 180 degrees

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

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

Angles on a straight line 180 degrees
Level 1-3

Angles around a point add up to 360\degree

angles around a point 360 degrees

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

angles around a point 360 degrees
Level 1-3

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

base angles isosceles triangle equal

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

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

base angles isosceles triangle equal
Level 1-3
Level 1-3

Example 1: Angles in a Triangle

Find the value of x in the triangle shown:

[2 marks] 

unknown angle in triangle

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

unknown angle in triangle
Level 1-3

Example 2: Finding a Missing Angle

Find the value of x in the triangle shown:

[2 marks]

unknown angle isosceles triangle

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

unknown angle isosceles triangle
Level 1-3

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Take an Online Exam

Geometry Problems Foundation Online Exam

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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