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 180 degrees](https://mmerevise.co.uk/app/uploads/2020/05/angles-in-a-triangle.png)
Angles in a triangle add up to 180\degree
![angles in a triangle 180 degrees](https://mmerevise.co.uk/app/uploads/2020/05/angles-in-a-triangle.png)
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 360 degrees](https://mmerevise.co.uk/app/uploads/2020/05/angles-in-a-quad.png)
Angles in a quadrilateral add up to 360\degree
![angles in a quadrilateral 360 degrees](https://mmerevise.co.uk/app/uploads/2020/05/angles-in-a-quad.png)
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
![angles around a point 360 degrees](https://mmerevise.co.uk/app/uploads/2020/05/angles-in-a-circle.png)
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
![base angles isosceles triangle equal](https://mmerevise.co.uk/app/uploads/2020/05/two-sides-of-a-triangle.png)
![base angles isosceles triangle equal](https://mmerevise.co.uk/app/uploads/2020/05/two-sides-of-a-triangle.png)
The two sides marked with the lines are the same length.
The two base angles, \textcolor{red}{x}, are the same.
![unknown angle in triangle](https://mmerevise.co.uk/app/uploads/2020/05/examlple-q1.png)
Example 1: Angles in a Triangle
Find the value of x in the triangle shown:
[2 marks]
![unknown angle in triangle](https://mmerevise.co.uk/app/uploads/2020/05/examlple-q1.png)
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 isosceles triangle](https://mmerevise.co.uk/app/uploads/2020/05/example-q2.png)
Example 2: Finding a Missing Angle
Find the value of x in the triangle shown:
[2 marks]
![unknown angle isosceles triangle](https://mmerevise.co.uk/app/uploads/2020/05/example-q2.png)
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
Geometry Basics Foundation Worksheet and Example Questions
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(NEW) Geometry Problems Foundation Exam Style Questions - MME
Level 1-3GCSENewOfficial MMEGeometry Basics Foundation Drill Questions
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Angles - Drill Questions
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Geometry Problems - Drill Questions
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