Year 8 - Maths
Perpendicular to a given line through a given point
Constructions
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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 we develop skills in using a pair of compasses and ruler to construct various accurate shapes and angles including triangles, rhombi, perpendicular lines and angle bisectors.
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.
- Shortest distances can be found using constructions with perpendicular lines.
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.
Common Mistakes To Avoid
- You can't accurately draw the perpendicular to a point on a line segment close to its endpoint.
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: You can't accurately draw the perpendicular to a point on a line segment close to its endpoint. Correction: The perpendicular to a line segment through any point can be found; some line segments just require extending in length first.
More Lessons In This Unit
- Bisecting an angle Study Guide
- Checking compass skills Study Guide
- Constructing rhombi Study Guide
- Constructing triangles Study Guide
- Diagonals of a rhombus Study Guide
- Perpendicular bisector of a line segment Study Guide
- Problem solving with constructions Study Guide
- Securing the skill of using a pair of compasses Study Guide
- Understanding constructing a circle Study Guide
Browse all guides in the Year 8 Maths guide library.