Year 11 - Maths
Constructing angles of 90° and 45°
Loci and construction
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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 construct triangles and construct diagrams following specific restrictions using their knowledge of loci and their work on constructions.
Lesson Summary
You will learn to construct angles of 90° and 45°.
Key Notes
- When constructing the perpendicular, you are constructing a 90° angle
- Bisecting a 90° angle results in two angles, each measuring 45°
Vocabulary To Learn
- Bisect: To bisect means to cut or divide an object into two equal parts.
- Complementary angles: Complementary angles are a pair of angles that sum to 90°.
- Supplementary angles: Supplementary angles are a pair of angles that sum to 180°.
- Conjugate angles: Conjugate angles are a pair of angles that sum to 360°.
Common Mistakes To Avoid
- Pupils may use a protractor rather than a pair of compasses.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When constructing the perpendicular, you are constructing a 90° angle. Bisecting a 90° angle results in two angles, each measuring 45°.
2. Use this key word in a maths sentence and explain it clearly. 'Bisect'
To bisect means to cut or divide an object into two equal parts. 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 use a protractor rather than a pair of compasses. Correction: Remind pupils that a construction is done using a pair of compasses and ruler.
More Lessons In This Unit
- Advanced problem solving with loci and constructions Study Guide
- Applying constructions to loci problems Study Guide
- Checking and securing understanding of bisecting an angle Study Guide
- Checking and securing understanding of constructing a perpendicular to a given line through a point Study Guide
- Checking and securing understanding of constructing the perpendicular bisector of a line segment Study Guide
- Constructing a right-angled triangle given the length of the hypotenuse and one other side length Study Guide
- Constructing a triangle given three side lengths using compasses Study Guide
- Constructing a triangle given two angles and the side length between them Study Guide
- Constructing a triangle given two side lengths and an angle not between them Study Guide
- Constructing a triangle given two side lengths and the angle between them using a compass Study Guide
- Constructing loci Study Guide
- Problem solving with loci and constructions Study Guide
- Solving loci problems in context Study Guide
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