Constructing a perpendicular bisector

The Maths Habit
Walkthrough to print

  1. Draw all the points that are 2.5 cm from P.

    P2.5 cmA circle,
    radius 2.5 cm

  2. Construct triangle ABC with AB = 5 cm, AC = 4 cm and angle A = 50°. Measure BC.

    AB50°CBC = 3.9 cm

  3. Construct triangle DEF with DE = 6 cm, angle D = 40° and angle E = 65°. Measure DF.

    DE40°65°FDF = 5.6 cm

Two friends live at A and B. They want a café exactly the same distance from both homes. Where could it be?

AB

Halfway is one answer, but so is any point on the line straight across the middle.

Bisect
Cut into two equal parts.
Perpendicular
At right angles.
Equidistant
The same distance from.

The perpendicular bisector of AB

  1. Open the compasses to more than half of AB.
  2. Arcs above and below AB from A.
  3. Keep the compasses the same width. Arcs from B.
  4. Join the two crossings.Every point on it is the same distance from A and B.
ABmore than half of AB

Construct the perpendicular bisector of AB. Leave your arcs showing. Arcs from both ends, the same width

AB

Construct the perpendicular bisector of CD. The arcs from C are drawn. Arcs from D, the same width

CD

Construct the perpendicular bisector of AB. Leave your arcs showing. Arcs from both ends, the same width

AB

Construct the perpendicular bisector of EF. The arcs from E are drawn. Arcs from F, the same width

EF

P is on the perpendicular bisector of AB. P is 5 cm from A. How far is P from B?

5 cm. Every point on the bisector is the same distance from A and B.

Closer to A or to B?

3 cm from A, 5 cm from B A

Which side of the bisector do you shade?

closer to B than to A B's side

Draw the locus of points that are the same distance from A as from B. The perpendicular bisector of AB

AB

Shade the region of points that are closer to A than to B. A's side of the bisector

AB

Draw the locus of points that are the same distance from A as from B. The perpendicular bisector of AB

AB

Children go to whichever school, A or B, is closer. Shade the part of the map whose children go to A. A's side of the bisector

ABmap

Draw the locus of points that are the same distance from A as from B. The perpendicular bisector of AB

AB

Construct the perpendicular bisector of PQ. Leave your arcs showing. Arcs from both ends, the same width

PQ

Draw the locus of points that are the same distance from A as from B. The perpendicular bisector of AB

AB

Draw the locus of points that are the same distance from C as from D. The perpendicular bisector of CD

CD

Draw the locus of points that are the same distance from A as from B. The perpendicular bisector of AB

AB

A park has two gates, G and H. Shade the part of the park that is nearer to H than to G. H’s side of the bisector

GHpark

Constructing a perpendicular bisector worksheet, page 1

Constructing a perpendicular bisector worksheet, page 2

Answer sheet

Thumbs up if it is right. Thumbs down if it is wrong.

  1. Every point on the perpendicular bisector of AB is the same distance from A and B.

    Right

  2. The compasses can be any width.

    Wrong

  3. The points closer to A are on the same side of the bisector as A.

    Right

  4. The perpendicular bisector only goes between A and B.

    Wrong

  1. Three towns make a triangle. A hospital must be the same distance from all three. How do you find where?

    Bisect two sides

  2. Use constructions to mark the point a quarter of the way along a line 8 cm long.

    Bisect twice

  3. Shape B is a reflection of shape A. How can a construction find the mirror line?

    Bisect point to image

  1. Construct the perpendicular bisector of AB. Leave your arcs showing.

    A line at 90° through the middle
    AB

  2. Shade the points closer to Q than to P.

    Q's side of the bisector
    PQ

  3. Kim sets her compasses to 3 cm to bisect a line 8 cm long. Explain why this will not work.

    3 cm is less than half of 8 cm
Exit tickets to print