Constructing an angle bisector

The Maths Habit
Walkthrough to print

Two straight fences meet at a corner. A dog runs so that it is always the same distance from both fences. Sketch its path.

fencefence

A straight line through the corner, splitting the angle exactly in half.

Bisect
Cut into two equal parts.
Arm
One of the two lines that make an angle.
Equidistant
The same distance from.

Angle bisector

  1. Draw the angleUse a protractor to draw the angle, or start from the angle you are given.
  2. Arc 1Point on the vertex.
    Draw one arc across both arms.
  3. Arc 2Point where the arc crosses one arm.
    Draw an arc between the arms.
  4. Arc 3Keep the same width.
    Do the same from the other arm.
  5. JoinRule a line from the vertex through the crossing.
    Leave your arcs showing.
  6. CheckTwo equal angles.
Walkthrough to print

An angle of 70° is bisected. How big is each half?

70° 35°

Each half is 28°. How big was the angle?

28° 56°

Construct the bisector of the angle. Leave your arcs showing. 30° each

30°30°

Construct the bisector of the angle. The first arc is drawn. 40° each

40°40°

Construct the bisector of the angle. Leave your arcs showing. 30° each

30°30°

Construct the bisector of the angle. The first arc is drawn. 50° each

50°50°

P is on the bisector of angle BAC. P is 2 cm from the line AB. How far is P from the line AC?

2 cm. Every point on the bisector is the same distance from both lines.

Which construction?

the same distance from two lines Angle bisector

Draw the locus of points that are the same distance from the line AB as from the line AC. The bisector of angle A

ABC

Shade the region inside angle BAC of points nearer to the line AB than to the line AC. AB's side of the bisector

ABC

Draw the locus of points that are the same distance from the line AB as from the line AC. The bisector of angle A

ABC

Hedges HX and HY meet at H.
Shade where sheep are nearer to HX than to HY. HX's side of the bisector

HXY

Construct the bisector of the angle. Leave your arcs showing. 30° each

30°30°

Construct the bisector of the angle. Leave your arcs showing. 35° each

35°35°

Draw the locus of points that are the same distance from the line AB as from the line AC. The bisector of angle A

ABC

Walls WX and WY meet at W.
Draw the locus of points the same distance from WX as from WY. The bisector of angle W

WXY

Draw the locus of points that are the same distance from the line AB as from the line AC. The bisector of angle A

ABC

Roads RS and RT meet at R.
Shade where a café is nearer to RT than to RS. RT's side of the bisector

RST

Constructing an angle bisector worksheet, page 1

Constructing an angle bisector worksheet, page 2

Answer sheet

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

  1. Every point on the bisector of angle A is the same distance from both arms.

    Right

  2. The arcs from the arms can be different widths.

    Wrong

  3. Bisecting 90° gives two angles of 45°.

    Right

  4. Points nearer to AB than AC are on the AC side of the bisector.

    Wrong

  1. Construct an angle of 45° using only compasses and a ruler.

    Bisect a right angle

  2. Draw a triangle. Bisect all three angles. What do you notice?

    They meet at one point

  3. Split an angle of 120° into four equal parts with constructions. How big is each?

    30°

  1. Construct the bisector of this angle. Leave your arcs showing.

    A line at 25° to each arm

  2. Which construction is equidistant from both lines? At what angle?

    Angle bisector, 35°
    70°

  3. Spot Ana's mistake.

    Arcs differ in size
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