Year 11 - Maths
Constructing a triangle given two side lengths and an angle not between them
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 from two side lengths and an angle not between them.
Key Notes
- The first side can be drawn accurately with a ruler
- All triangles with these measurements in the same place are congruent
- The angle should be accurately measured with a protractor
- Two different triangles can be drawn with these measurements
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 not use a pair of compasses to find the two positions of the third vertex and instead just try to use their ruler.
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. All triangles with these measurements in the same place are congruent.
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 not use a pair of compasses to find the two positions of the third vertex and instead just try to use their ruler. Correction: You could encourage them to draw the circle before the angle each time.
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 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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