# Geometry Basics Foundation

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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.

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## Angles in a triangle add up to $180\degree$

The angles in a triangle add up to $180\degree$

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

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## Angles in a quadrilateral add up to $360\degree$

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

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

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## Angles on a straight line add up to $180\degree$

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

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

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## Angles around a point add up to $360\degree$

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

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

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## 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.

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## 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 $180\degree$,

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

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

$x= 60\degree$

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## 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:

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

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

$2x = 130\degree$

$x\degree = 65\degree$

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## Geometry Basics Foundation 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}

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

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

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

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

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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}

$x=62.5\degree$

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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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## Geometry Basics Foundation Worksheet and Example Questions

### (NEW) Geometry Problems Foundation Exam Style Questions - MME

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## Geometry Basics Foundation Drill Questions

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### Geometry Problems - Drill Questions

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