Year 11 - Maths
Applying constructions to loci problems
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 apply the rules for constructing angle and line bisectors to loci problems.
Key Notes
- The perpendicular bisector of a line segment divides the line segment into two equal parts
- The perpendicular bisector is the same distance from each end point of the line segment
- If you only had the two end points, the perpendicular bisector would still be the same distance from each point
- The bisector of an angle divides the angle into two equal parts.
Vocabulary To Learn
- Bisect: To bisect means to cut or divide an object into two equal parts.
- Loci: A locus is a set of points that satisfy a given set of conditions. Multiple sets of points are referred to as loci.
- Equidistant: Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.
Common Mistakes To Avoid
- Pupils may believe that there is only one point which is equidistant from two points.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The perpendicular bisector of a line segment divides the line segment into two equal parts. The perpendicular bisector is the same distance from each end point of the line segment.
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 believe that there is only one point which is equidistant from two points. Correction: Highlight that forming any isosceles triangle will mean that that the point is equidistant from both points.
More Lessons In This Unit
- Advanced problem solving with loci and constructions 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 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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