Year 9 - Maths
Checking and securing understanding of similar triangles
Trigonometry
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils learn how to recognise the relationship between the unit circle and the trigonometric ratios of sine, cosine and tangent. Pupils then apply this knowledge to solve trigonometric problems.
Lesson Summary
You will learn to recognise that similar shapes have sides in proportion to each other but angle sizes are preserved.
Key Notes
- An enlargement means a change in size.
- The lengths of the lines may change when enlarged.
- The angles inside an object do not change when enlarged.
- When an object is enlarged, the image is similar.
Vocabulary To Learn
- Similar: Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.
- Enlargement: Enlargement is a transformation that causes a change of size.
- Scale factor: Scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.
Common Mistakes To Avoid
- You need to know all the lengths or all of the angles in a pair of triangles to know that they are similar.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
An enlargement means a change in size. The lengths of the lines may change when enlarged.
2. Use this key word in a maths sentence and explain it clearly. 'Similar'
Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: You need to know all the lengths or all of the angles in a pair of triangles to know that they are similar. Correction: Remind pupils that they do not necessarily need to know all of the length and angles to determine whether two triangles are congruent, so they don't all need to be known to determine similarity.
More Lessons In This Unit
- Checking and securing understanding of Pythagoras' theorem Study Guide
- Choosing an appropriate method for finding lengths of a triangle Study Guide
- Choosing the right trigonometric ratio Study Guide
- Problem solving with trigonometry Study Guide
- Scaling the right-angled triangle from the unit circle Study Guide
- Sine and cosine ratios Study Guide
- Tangent ratio Study Guide
- The unit circle Study Guide
- Using the cosine ratio Study Guide
- Using the sine ratio Study Guide
- Using the tangent ratio Study Guide
Browse all guides in the Year 9 Maths guide library.