Bisecting an angle
I can use the properties of a rhombus to construct an angle bisector.
Bisecting an angle
I can use the properties of a rhombus to construct an angle bisector.
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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.
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
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.
To help you plan your year 8 maths lesson on: Bisecting an angle, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 8 maths lesson on: Bisecting an angle, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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Equipment
Licence
Prior knowledge starter quiz
6 Questions
Q1.This quadrilateral is a rhombus. What is the size of angle $$x$$?

Q2.This quadrilateral is a rhombus. What is the size of angle $$r$$?

Q3.This quadrilateral is a rhombus. What is the perimeter of this rhombus (in cm)?

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?

Q5.Both rhombi are congruent, with the right-hand rhombus having both diagonals drawn on. Match the angles in the rhombus to its size.

$$a$$ -
118°
$$b$$ -
31°
$$c$$ -
59°
$$d$$ -
90°
Q6.Which of these quadrilaterals have the correct feathers, hash marks, and/or angle markers that confirm the shape is a rhombus?

Assessment exit quiz
6 Questions
Q1.Which of these diagrams shows the compass width being accurately set to 5 cm?

Q2.What is the value of $$r$$, the radius of the circle drawn?

Q3.Which statements are correct about this construction?

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?

Q5.This diagram shows the correct constructions to bisect an angle. Which point of intersection between two circles must the bisecting line pass through?

Q6.Which of these construction arcs could be the first to be drawn in a construction to bisect an angle?
