New
New
Year 11
Higher

Checking and securing understanding of bisecting an angle

I can use the properties of a rhombus to construct an angle bisector.

New
New
Year 11
Higher

Checking and securing understanding of bisecting an angle

I can use the properties of a rhombus to construct an angle bisector.

Lesson details

Key learning points

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

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.

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.

When bisecting an angle through construction, ensure that students do not use a protractor to aid in their construction. A protractor should only be used after the construction is completed in order to check the precision of their construction.
Teacher tip

Equipment

Pair of compasses, protractor and 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.
A perpendicular bisector of the line PQ is a line that is at an angle of ° to PQ. It cuts PQ exactly in half.
Correct Answer: 90
Q2.
Izzy has incorrectly constructed a perpendicular for PQ through R. What is wrong with Izzy's construction?
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Correct answer: The line segment PQ should touch the circle twice.
Correct answer: 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.
Correct answer: The line through R may not be perpendicular to PQ.
Q3.
Which of these circles does not help in the construction of the perpendicular to LM through point P?
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Correct answer: Circle a
Circle b
Circle c
Q4.
Laura has partially completed a construction for a perpendicular of AB through O. What is incorrect about Laura’s pair of compasses?
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The compass width is too wide.
Correct answer: 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.
Q5.
The diagram shows the perpendicular through Z to the line segment SR. The radius of the circle is cm.
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Correct Answer: 12
Q6.
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.
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Correct Answer: 14 cm

6 Questions

Q1.
Aisha constructs the bisector of an angle of 72°. Aisha has made angles of °.
Correct Answer: 36
Q2.
The diagram shows two congruent isosceles triangles put together to form a rhombus. Match each angle to its size.
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Correct Answer:$$a$$°,22°

22°

Correct Answer:$$b$$°,44°

44°

Correct Answer:$$c$$°,136°

136°

Correct Answer:Not a marked angle,64°

64°

Q3.
Starting with the first step, put these steps in order to construct a rhombus given the legs of an angle.
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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.
Q4.
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.
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Correct Answer: 11
Q5.
Alex begins construction of a rhombus from this angle. The final vertex of the rhombus is at point .
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Correct Answer: B, b
Q6.
Sam is constructing an angle bisector. Here are the construction marks. Which two arcs did Sam draw first?
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Correct answer: a
b
Correct answer: c
d