Year 9 - Maths
Congruent triangles (SAS)
Geometrical properties: similarity and Pythagoras' theorem
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Study Guides
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 (SAS).
Key Notes
- By knowing two side lengths and the angle between them in the triangle and image, you can prove congruence.
- The angle between the sides must be the same in both object and image.
- The given sides must have the same multiplicative relationship.
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 believe that the angle doesn't need to be in between the two known sides.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
By knowing two side lengths and the angle between them in the triangle and image, you can prove congruence. The angle between the sides must be the same in both object and image.
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 believe that the angle doesn't need to be in between the two known sides. Correction: Use the Geogebra files to demonstrate that more than one triangle can be formed at times, and therefore it does not guarantee congruence between two triangles.
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 (ASA and AAS) Study Guide
- Congruent triangles (RHS) 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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