Checking and securing understanding of bisecting an angle | Maths

Starter quiz

A perpendicular bisector of the line PQ is a line that is at an angle of ______° to PQ. It cuts PQ exactly in half.

'90' ✓
Izzy has incorrectly constructed a perpendicular for PQ through R. What is wrong with Izzy's construction?

The line segment PQ should touch the circle twice. ✓

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

It is only possible to draw a perpendicular through the midpoint of PQ.

The whole diagram has been rotated.

The line through R may not be perpendicular to PQ. ✓
Which of these circles does not help in the construction of the perpendicular to LM through point P?

Circle a ✓

Circle b

Circle c
Laura has partially completed a construction for a perpendicular of AB through O. What is incorrect about Laura’s pair of compasses?

The compass width is too wide.

The compass width is too short. ✓

The compass needle should be at point A.

The compass needle should be at point B.

The compass needle should be at point O.
The diagram shows the perpendicular through Z to the line segment SR. The radius of the circle is ______ cm.

'12' ✓
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.

'14 cm' ✓

Exit quiz

Aisha constructs the bisector of an angle of 72°. Aisha has made angles of ______°.

'36' ✓
The diagram shows two congruent isosceles triangles put together to form a rhombus. Match each angle to its size.

$a$ °

⇔

22° ✓

$b$ °

⇔

44° ✓

$c$ °

⇔

136° ✓

Not a marked angle

⇔

64° ✓
Starting with the first step, put these steps in order to construct a rhombus given the legs of an angle.

1

⇔

Set your compasses to a width equal to the shorter of the two legs.

2

⇔

Place your compass needle on the vertex of the angle.

3

⇔

Make an arc on each leg.

4

⇔

Place the compass needle on the arc of one leg created in the previous step.

5

⇔

Place the pencil on the vertex of the angle. Draw a circle.

6

⇔

Repeat on the open endpoint of the other leg.

7

⇔

Use a ruler to connect the points to form a rhombus.
Jun wants to construct a rhombus using an angle with leg lengths of 11 cm and 17 cm. The maximum radius of each circle in the construction of this rhombus is ______ cm.

'11' ✓
Alex begins construction of a rhombus from this angle. The final vertex of the rhombus is at point ______.

'B' ✓
Sam is constructing an angle bisector. Here are the construction marks. Which two arcs did Sam draw first?

a ✓

b

c ✓

d

Worksheet

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Lesson Details

Key learning points

A rhombus can be constructed from two congruent isosceles triangles
The diagonals of a rhombus bisect the angles
It is possible to construct an angle bisector without drawing the rhombus
The angle could be the interior angle of a shape

Common misconception

"My construction didn't accurately bisect the angle"

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.