Year 11 - Maths
Constructing a triangle given three side lengths using compasses
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 triangle given the three required side lengths.
Key Notes
- The first side can be drawn accurately with a ruler
- A pair of compasses should be used to indicate potential positions for the other sides, by drawing arcs
- Where the two remaining sides intersect is where the two sides should be drawn to
- 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.
- Radius: The radius is any line segment that joins the centre of a circle to any point on its circumference.
- Congruent: If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
- Arc: An arc is part of a curve. An arc of a circle is part of the circle's circumference.
Common Mistakes To Avoid
- Pupils may try to draw the triangle using only a pencil and ruler, rather than construct it using 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.
The first side can be drawn accurately with a ruler. A pair of compasses should be used to indicate potential positions for the other sides, by drawing arcs.
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 try to draw the triangle using only a pencil and ruler, rather than construct it using a pair of compasses. Correction: Remind pupils that if the task is to 'construct' then they must use their geometry equipment.
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 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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