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Perpendicular bisector of a line segment
I can use the properties of a rhombus to construct a perpendicular bisector of a line segment.
Lesson 8 of 10
New
New
- Year 8
Perpendicular bisector of a line segment
I can use the properties of a rhombus to construct a perpendicular bisector of a line segment.
Lesson details
Key learning points
- A rhombus can be constructed from two congruent isosceles triangles.
- The diagonals of a rhombus meet at right angles and bisect each other.
- It is possible to construct the perpendicular bisector of a line segment 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.
Common misconception
I can use a ruler to measure the midpoint of a line segment, and a protractor to find 90°.
Constructions, such as perpendicular bisectors, are methods of creating & modifying shapes & angles in ways that don't require measurements.
When checking that the radius of each circle or arc constructed is equal (and in cases where its length is important), it might help to get students to draw a reference line that can be used to readjust the compass width after each arc is drawn.
Teacher tip
Licence
This content is © Oak National Academy Limited (2025), 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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Prior knowledge starter quiz
6 Questions
Q1.This quadrilateral is a rhombus with one of its diagonals drawn on. What is the size of angle $$p$$?
This quadrilateral is a rhombus with one of its diagonals drawn on. What is the size of angle $$p$$?
Correct Answer: 43, 43°, 43 degrees
43, 43°, 43 degrees
Q2.This quadrilateral is a rhombus with one of its diagonals drawn on. What is the size of angle $$m$$?
This quadrilateral is a rhombus with one of its diagonals drawn on. What is the size of angle $$m$$?
35°
55°
70°
Correct answer: 110°
110°
220°
Q3.This quadrilateral is a rhombus with both of its diagonals drawn on. Match the angles in the rhombus to its size.
This quadrilateral is a rhombus with both of its diagonals drawn on. Match the angles in the rhombus to its size.
Correct Answer:$$a$$,22°
$$a$$ - 22°
Correct Answer:$$b$$,44°
$$b$$ - 44°
Correct Answer:$$c$$,68°
$$c$$ - 68°
Correct Answer:$$d$$,90°
$$d$$ - 90°
Q4.What is the area of this rhombus?
What is the area of this rhombus?
30 cm²
40 cm²
Correct answer: 48 cm²
48 cm²
240 cm²
Q5.A rhombus has side length of 41 cm, and diagonals of length 18 cm and 80 cm. What is the area of this rhombus (in cm²)?
A rhombus has side length of 41 cm, and diagonals of length 18 cm and 80 cm. What is the area of this rhombus (in cm²)?
Correct Answer: 1440, 1440 cm², 1440cm²
1440, 1440 cm², 1440cm²
Q6.This triangle is reflected with the line of reflection at its base side. The resultant quadrilateral is a rhombus. What is the area of this rhombus (in cm²)?
This triangle is reflected with the line of reflection at its base side. The resultant quadrilateral is a rhombus. What is the area of this rhombus (in cm²)?
Correct Answer: 240, 240 cm², 240cm²
240, 240 cm², 240cm²
Assessment exit quiz
6 Questions
Q1.Which of these diagrams show a perpendicular bisector on a rhombus?
Which of these diagrams show a perpendicular bisector on a rhombus?
a
Correct answer: b
b
c
Correct answer: d
d
e
Q2.Which of these compass widths are suitable when constructing the perpendicular bisector of the given line segment?
Which of these compass widths are suitable when constructing the perpendicular bisector of the given line segment?
a
Correct answer: b
b
Correct answer: c
c
Q3.Which of these constructions can be used to draw on the perpendicular bisector of the line segment given?
Which of these constructions can be used to draw on the perpendicular bisector of the line segment given?
Correct answer: a
a
b
c
Correct answer: d
d
e
Q4.Each of the two circles has been drawn with a radius of 7 cm, one with centre Y, and the other with centre Z. Match the statement to the point it describes.
Each of the two circles has been drawn with a radius of 7 cm, one with centre Y, and the other with centre Z. Match the statement to the point it describes.
Correct Answer:point A,7 cm away from Y and greater than 7 cm away from Z.
point A - 7 cm away from Y and greater than 7 cm away from Z.
Correct Answer:point B,7 cm away from Y and less than 7 cm away from Z.
point B - 7 cm away from Y and less than 7 cm away from Z.
Correct Answer:point C,7 cm away from Z and greater than 7 cm away from Y.
point C - 7 cm away from Z and greater than 7 cm away from Y.
Correct Answer:point D,7 cm away from both Y and Z.
point D - 7 cm away from both Y and Z.
Q5.Lucas wants to construct the perpendicular bisector of line segment RS, which has a length of 18 cm. Which of these construction methods are possible?
Lucas wants to construct the perpendicular bisector of line segment RS, which has a length of 18 cm. Which of these construction methods are possible?
Constructing arcs of radius 6 cm at both points R and S.
Constructing arcs of radius 9 cm at both points R and S.
Correct answer: Constructing arcs of radius 12 cm at both points R and S.
Constructing arcs of radius 12 cm at both points R and S.
Correct answer: Constructing arcs of radius 18 cm at both points R and S.
Constructing arcs of radius 18 cm at both points R and S.
Constructing an arc of radius 12 cm at R and an arc of radius 18 cm at S.
Q6.Which of these statements is true about this construction?
Which of these statements is true about this construction?
A perpendicular bisector to YZ has definitely been constructed.
A perpendicular bisector to YZ has definitely not been constructed.
Correct answer: The construction of the perpendicular bisector to YZ is incomplete.
The construction of the perpendicular bisector to YZ is incomplete.
The angle between the two line segments is 88°.
Correct answer: Two more arcs need to be constructed.
Two more arcs need to be constructed.
