New
New
Year 8

Bisecting an angle

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

New
New
Year 8

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.

Common misconception

I can use a protractor to measure an angle, then half that angle to bisect it.

Constructions, such as bisecting an angle, are methods of creating & modifying shapes & angles in ways that don't require measurement tools.

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.

When bisecting a reflex angle, a student can bisect the conjugate angle, and extend the line of bisection through to the reflex part of the diagram.
Teacher tip

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).

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6 Questions

Q1.
This quadrilateral is a rhombus. What is the size of angle $$x$$?
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Correct Answer: 128, 128 degrees, 128degrees, 128°
Q2.
This quadrilateral is a rhombus. What is the size of angle $$r$$?
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Correct Answer: 28, 28 degrees, 28degrees, 28°
Q3.
This quadrilateral is a rhombus. What is the perimeter of this rhombus (in cm)?
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Correct Answer: 144, 144 cm, 144cm
Q4.
The rhombus on the right is congruent to the rhombus on the left, with one diagonal drawn. Which of these statements correctly describes the rhombus after its diagonal has been drawn on?
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The rhombus has been split into two scalene triangles.
Correct answer: The rhombus has been split into two isosceles triangles.
Correct answer: The angle of 80° has been bisected.
Correct answer: The angle of 80° has been cut exactly in half.
All angles in the rhombus are now 40°.
Q5.
Both rhombi are congruent, with the right-hand rhombus having both diagonals drawn on. Match the angles in the rhombus to its size.
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Correct Answer:$$a$$,118°

118°

Correct Answer:$$b$$,31°

31°

Correct Answer:$$c$$,59°

59°

Correct Answer:$$d$$,90°

90°

Q6.
Which of these quadrilaterals have the correct feathers, hash marks, and/or angle markers that confirm the shape is a rhombus?
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a
Correct answer: b
c
d
Correct answer: e

6 Questions

Q1.
Which of these diagrams shows the compass width being accurately set to 5 cm?
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a
Correct answer: b
c
Q2.
What is the value of $$r$$, the radius of the circle drawn?
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Correct Answer: 3.6, 3.6 cm, 3.6cm
Q3.
Which statements are correct about this construction?
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A rhombus has been constructed as both legs of the angle are of equal length.
A rhombus has been constructed as both circles use endpoints A and B as centres.
Correct answer: A rhombus hasn't been constructed as all four sides aren't of equal length.
Correct answer: A rhombus hasn't been constructed as both circles are not the same size.
A rhombus hasn't been constructed as a pair of compasses haven't been used.
Q4.
The two legs of the angle are different in length. Which compass placement is correct in order to create a pair of shorter legs of equal length?
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Correct answer: a
b
c
Q5.
This diagram shows the correct constructions to bisect an angle. Which point of intersection between two circles must the bisecting line pass through?
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a
b
Correct answer: c
d
e
Q6.
Which of these construction arcs could be the first to be drawn in a construction to bisect an angle?
An image in a quiz
Correct answer: a
b
c
Correct answer: d