Year 11 - Maths
Checking and securing understanding of constructing a perpendicular to a given line through a point
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 use the properties of a rhombus to construct a perpendicular to a given line through a given point.
Key Notes
- A rhombus can be constructed from two congruent isosceles triangles.
- This can be used to construct a perpendicular to a line through a point.
- This perpendicular has special properties that can be investigated.
- The line and point could be part of a shape.
Vocabulary To Learn
- Bisect: To bisect means to cut or divide an object into two equal parts.
- Rhombus: A rhombus is a parallelogram where all sides are the same length.
- 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
- "My construction didn't accurately bisect the line segment"
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A rhombus can be constructed from two congruent isosceles triangles. This can be used to construct a perpendicular to a line through a point.
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: "My construction didn't accurately bisect the line segment". Correction: Check that your compasses construct a full circle, and do not slip (and create a spiral-shape). Tighten the screw on your compasses, if possible. Then, if only using construction arcs that look confusing, you can construct full circles to help.
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 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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