Perpendicular to a given line through a given point

Maths

Checking compass skills

Securing the skill of using a pair of compasses

Understanding constructing a circle

Constructing triangles

Constructing rhombi

Diagonals of a rhombus

Bisecting an angle

Perpendicular bisector of a line segment

Problem solving with constructions

The constructions covered in this unit are built on in the future unit. In the future unit, pupils construct triangles and construct diagrams following specific restrictions.

The prior unit gave pupils the opportunity to explore polygons and begin to generalise their understanding of interior/exterior angles in regular polygons. In this unit, pupils will use the geometrical properties of a rhombus to perform various constructions. 

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.

Constructions

The line segment EF has been shortened by constructing a circle of radius 8 cm, with a centre at point K. What is the length (in cm) of the shortened line segment?

Which of these diagrams shows the most appropriate first step when constructing the perpendicular to line segment TU through point Z?

Izzy has shortened line segment LM by drawing a circle with centre at point Z. Izzy wants to draw four arcs of radius $$k$$ cm to construct a perpendicular. What value must $$k$$ be greater than?

A line segment is extended so that a perpendicular can be constructed through point Z. Which of these diagrams shows a suitable extension of the line segment?

Which of these four circles can help in the construction of the perpendicular to line segment WU through point Z?

the shortest distance from X to an extension of JK

the shortest distance from X to line segment JK

the radius of circle with centre at point X

This quadrilateral is a kite. Find the value of angle $$a$$, in degrees.

This diagram shows an accurate construction of a perpendicular bisector. YZ has a length of 8.4 cm. Which of these is the smallest value of $$r$$ that can be used in this construction?

A perpendicular bisector to line segment QV

A line segment connecting the intersection to point Z.

A line through two pairs of intersecting arcs.

This is an incomplete construction to find the perpendicular bisector of YZ. Which of these steps is missing from this construction?

This is an accurate construction to draw a rhombus. What is the perimeter (in cm) of the rhombus that can be drawn from this construction?

Sofia needs to place the compass needle at the midpoint of EF.

Sofia should draw a circle with centre at the intersection of EF and the circle.

Sofia needs to draw an arc with centre at point F next.

Sofia should adjust the compass width so that both circles drawn are congruent.

Currently, the next circle Sofia draws will be smaller than the first.

Sofia starts her construction of a perpendicular bisector to EF. She is about to move the pair of compoasses to construct a second circle. Which of these statements are true?

Perpendicular to a given line through a given point

Lesson outcome