Year 11 - Maths
Constructing a right-angled triangle given the length of the hypotenuse and one other side length
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 a right-angled triangle given the length of the hypotenuse and one other side length.
Key Notes
- The shorter side can be drawn accurately with a ruler
- The perpendicular through the end point of the drawn side should be constructed
- The compass should be used to indicate potential positions for the hypotenuse
- All triangles with the same measurements are congruent
Vocabulary To Learn
- Pair of compasses: A pair of compasses is a tool which can be used to draw circles and arcs. A pair of compasses is sometimes referred to just as a compass.
- 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 want to use a protractor to draw a right angle.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The shorter side can be drawn accurately with a ruler. The perpendicular through the end point of the drawn side should be constructed.
2. Use this key word in a maths sentence and explain it clearly. 'Pair of compasses'
A pair of compasses is a tool which can be used to draw circles and arcs. A pair of compasses is sometimes referred to just as a compass. 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 want to use a protractor to draw a right angle. Correction: Remind pupils that they need to construct the right angle with a pair of compasses and a ruler, using appropriate construction techniques.
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 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 angles of 90° and 45° 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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