Year 10 - Maths
Checking and securing understanding of congruent triangles (RHS)
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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 investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape.
Lesson Summary
You will learn to understand and use the criteria by which triangles are congruent (RHS).
Key Notes
- For a right-angled triangle, you need the hypotenuse and one other side length to prove congruence.
- Right-angled triangles, by definition, have a right-angle.
- There is a special relationship between the sides in a right-angled triangle.
Vocabulary To Learn
- Congruent: If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
- Similar: Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.
- Pythagoras' theorem: Pythagoras' theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.
Common Mistakes To Avoid
- Pupils may make incorrect assumptions about diagrams containing a right angle.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
For a right-angled triangle, you need the hypotenuse and one other side length to prove congruence. Right-angled triangles, by definition, have a right-angle.
2. Use this key word in a maths sentence and explain it clearly. 'Congruent'
If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may make incorrect assumptions about diagrams containing a right angle. Correction: Remind pupils that they cannot assume there is a right angle, just because two line segments look as if they are perpendicular to each other.
More Lessons In This Unit
- Checking and securing understanding of congruent triangles (ASA) Study Guide
- Checking and securing understanding of congruent triangles (SAS) Study Guide
- Checking and securing understanding of congruent triangles (SSS) Study Guide
- Checking and securing understanding of direct proportion in context Study Guide
- Problem solving with advanced similarity knowledge Study Guide
- Problem solving with similarity Study Guide
- The effect of enlargement on the area of a shape Study Guide
- The effect of enlargement on the perimeter of a shape Study Guide
- The effect of enlargement on the volume of a 3D shape Study Guide
- Using the scale factor for enlarging a volume Study Guide
- Using the scale factor for enlarging an area Study Guide
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