Geometry Basics Foundation

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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.

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angles in a triangle 180 degrees

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

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angles in a quadrilateral 360 degrees

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

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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

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

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

base angles isosceles triangle equal
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.

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unknown angle in triangle

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

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unknown angle isosceles triangle

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

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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] 

 

unknown angle on straight line

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

[2 marks] unknown angle around point

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

Give a reason for your answer.

[2 marks] 

unknown angle isosceles triangle

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

Give a reason for your answer.

[2 marks] 

 

unknown base angle isosceles triangle

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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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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] 

unknown angle on straight line with triangle

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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

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(NEW) Geometry Problems Foundation Exam Style Questions - MME

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Geometry Basics Foundation Drill Questions

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Angles - Drill Questions

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Geometry Problems - Drill Questions

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