Year 9 - Maths
Applying the criteria for congruence
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 identify congruent triangles and prove why they are congruent.
Key Notes
- If two triangles are congruent, then one of the proven criteria must apply.
- By stating the criteria (that you have already proven), you can prove congruence.
- It is important to be clear why you know that two triangles are congruent.
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 think they need to know the actual size or length to be able to prove congruence.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
If two triangles are congruent, then one of the proven criteria must apply. By stating the criteria (that you have already proven), you can prove congruence.
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 think they need to know the actual size or length to be able to prove congruence. Correction: Remind pupils that if they can show that the corresponding angles or sides are the same length, then that is all that is needed. For example, if the corresponding edges are both edges of the same regular polygon, then they will be the same.
More Lessons In This Unit
- Checking understanding of congruence Study Guide
- Checking understanding of similarity Study Guide
- Congruence in shapes Study Guide
- Congruent triangles (ASA and AAS) 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
Browse all guides in the Year 9 Maths guide library.