New
New
Year 11
Higher

Constructing angles of 90° and 45°

I can construct angles of 90° and 45°.

New
New
Year 11
Higher

Constructing angles of 90° and 45°

I can construct angles of 90° and 45°.

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Lesson details

Key learning points

  1. When constructing the perpendicular, you are constructing a 90° angle
  2. Bisecting a 90° angle results in two angles, each measuring 45°

Keywords

  • Bisect - To bisect means to cut or divide an object into two equal parts.

  • Complementary angles - Complementary angles are a pair of angles that sum to 90°.

  • Supplementary angles - Supplementary angles are a pair of angles that sum to 180°.

  • Conjugate angles - Conjugate angles are a pair of angles that sum to 360°.

Common misconception

Pupils may use a protractor rather than a pair of compasses.

Remind pupils that a construction is done using a pair of compasses and ruler.

Pupils could create their own questions for peers to complete.
Teacher tip

Equipment

Pair of compasses, protractor, ruler.

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
Andeep constructs the bisector of an angle of 104°. Andeep has made angles of °.
Correct Answer: 52
Q2.
The diagram shows two congruent isosceles triangles put together to form a rhombus. Match each angle to its size.
An image in a quiz
Correct Answer:$$a$$°,32°

32°

Correct Answer:$$b$$°,64°

64°

Correct Answer:$$c$$°,116°

116°

Correct Answer:Not a marked angle,44°

44°

Q3.
Here are the steps to construct a rhombus given the legs of an angle. Match each step to the correct instruction.
An image in a quiz
Correct Answer:Step 1,Set your compasses to a width equal to the shorter of the two legs.

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

Correct Answer:Step 2,Place your compass needle on the vertex of the angle.

Place your compass needle on the vertex of the angle.

Correct Answer:Step 3,Make an arc on each leg, then place the compass needle on one arc.

Make an arc on each leg, then place the compass needle on one arc.

Correct Answer:Step 4,Place the pencil on the vertex of the angle. Draw a circle.

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

Correct Answer:Step 5,Repeat on the open endpoint of the other leg.

Repeat on the open endpoint of the other leg.

Correct Answer:Step 6,Draw lines with a ruler to connect the points to form a rhombus.

Draw lines with a ruler to connect the points to form a rhombus.

Q4.
Jacob wants to construct a rhombus using an angle with leg lengths of 10 cm and 15 cm. The maximum radius of each circle in the construction of this rhombus is cm.
An image in a quiz
Correct Answer: 10
Q5.
Lucas begins construction of a rhombus from this angle. Which point is the final vertex of the rhombus?
An image in a quiz
A
Correct answer: B
C
D
Q6.
Jun is constructing an angle bisector. Here are the construction marks. Which two arcs did Jun draw first?
An image in a quiz
Correct answer: a
b
Correct answer: c
d

6 Questions

Q1.
Complementary angles are a pair of angles that sum to °.
Correct Answer: 90
Q2.
The diagram shows the perpendicular to UV that passes through the point T. The perpendicular intersects UV at point S. Which of these constructions will produce a 45° angle?
An image in a quiz
The perpendicular bisector of ST.
The perpendicular bisector of TV.
Correct answer: The angle bisector of UST.
The angle bisector of UTV
Correct answer: The angle bisector of TSV.
Q3.
EC is a perpendicular to BD. The angle BOE is bisected. Match each angle to its size.
An image in a quiz
Correct Answer:Angle BOC,90°

90°

Correct Answer:Angle AOE,45°

45°

Correct Answer:Angle AOD,135°

135°

Correct Answer:Reflex angle AOE,315°

315°

Correct Answer:Reflex angle AOD,225°

225°

Q4.
The line segments AB and BC form an angle of 110°. Which of these constructions creates a 55° angle?
An image in a quiz
The perpendicular bisector of BC.
A perpendicular to AB through B.
An extension of AB in the direction of B.
Correct answer: An angle bisector of the angle ABC.
Q5.
Line segments AB and BC are the legs of a 124° angle. The diagram shows the two constructions that are applied to ABC. The angle $$x$$° is °.
An image in a quiz
Correct Answer: 28
Q6.
Line segments AB and BC are the legs of a 124° angle. The diagram shows the two constructions that are applied to ABC. The angle $$z$$° is °.
An image in a quiz
Correct Answer: 118