Checking and securing understanding of constructing a perpendicular to a given line through a point | Maths

Starter quiz

To bisect means to cut or divide an object into ______ equal parts.

'two' ✓
Which of these is not a property of any rhombus?

Diagonals are equal length ✓

Diagonals meet at right-angles

2 lines of symmetry

4 lines of symmetry ✓
Two triangles are put together to form a quadrilateral. Which quadrilateral is a rhombus?
Aisha correctly draws three of the four arcs needed to construct the perpendicular bisector of LM. Point A is 6 cm away from point L. Point B is ______ cm away from point M.

'6' ✓
Lucas correctly draws three of the four arcs needed to construct the perpendicular bisector of AB. Point C is ______ from A and B.

'equidistant' ✓
Which of these diagrams show an accurate construction of a perpendicular bisector of the line segment PQ?

Exit quiz

A perpendicular to the line AB is a line that is at an angle of ______° to AB.

'90' ✓
Sam has incorrectly constructed a perpendicular for LM through P. What is wrong with Sam's construction?

The whole diagram has been rotated.

The circle only touches the line segment LM once. ✓

Sam hasn’t drawn all the expected construction arcs. ✓

The line through P may not be perpendicular to LM. ✓

It is only possible to draw a perpendicular through the midpoint of LM.
Which of these circles will help in the construction of the perpendicular to AB through point P.

Circle a

Circle b ✓

Circle c ✓
Jun has partially completed a construction for a perpendicular of QR through P. What is incorrect about Jun’s pair of compasses?

The compass needle should be at point Q.

The compass needle should be at point P.

The compass needle should be at point R.

The compass width is too short. ✓

The compass width is too wide.
The diagram shows the perpendicular through Z to the line segment SR. The shortest distance from Z to an extension of line segment SR is ______ cm.

'8' ✓
The diagram shows the perpendicular through Z to the line segment SR. The shortest distance from Z to the original line segment SR is ______ cm.

'13' ✓

Worksheet

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Lesson Details

Key learning points

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.

Common misconception

"My construction didn't accurately bisect the line segment"

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.

Keywords

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.