Year 9 - Maths
Congruent triangles (ASA and AAS)
Geometrical properties: similarity and Pythagoras' theorem
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
This unit explores the concepts of congruence and similarity, and ways to prove or disprove similarity between shapes. We then explore further properties of triangles with Pythagoras' Theorem.
Lesson Summary
You will learn to appreciate and use the criteria by which triangles are congruent (ASA and AAS).
Key Notes
- By knowing two angles and a length in the triangle and image, you can prove congruence.
- The angle pairs must be identical.
- This rule is derived from the SAS criteria for congruence.
Vocabulary To Learn
- Congruent: If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
Common Mistakes To Avoid
- Pupils may struggle to spot congruent triangles if they only look for ASA.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
By knowing two angles and a length in the triangle and image, you can prove congruence. The angle pairs must be identical.
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 struggle to spot congruent triangles if they only look for ASA. Correction: Encourage pupils to add any further information to diagrams, like the third angle, before starting to prove congruence.
More Lessons In This Unit
- Applying the criteria for congruence Study Guide
- Checking understanding of congruence Study Guide
- Checking understanding of similarity Study Guide
- Congruence in shapes Study Guide
- Congruent triangles (RHS) Study Guide
- Congruent triangles (SAS) Study Guide
- Congruent triangles (SSS) Study Guide
- Congruent, similar or neither Study Guide
- Demonstrating Pythagoras' theorem Study Guide
- Determining which side Study Guide
- Further demonstrating of Pythagoras' theorem Study Guide
- Length of a shorter side Study Guide
- Length of the hypotenuse Study Guide
- Problem solving with similarity and Pythagoras' theorem Study Guide
- Pythagoras' theorem in context Study Guide
- Rotational symmetry Study Guide
- Similarity in shapes Study Guide
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