Perpendicular bisector of a line segment | Maths | Quizalize & Oak National Academy

Starter quiz

This quadrilateral is a rhombus with one of its diagonals drawn on. What is the size of angle $p$ ?

'43' ✓
This quadrilateral is a rhombus with one of its diagonals drawn on. What is the size of angle $m$ ?

35°

55°

70°

110° ✓

220°
This quadrilateral is a rhombus with both of its diagonals drawn on. Match the angles in the rhombus to its size.

$a$

⇔

22° ✓

$b$

⇔

44° ✓

$c$

⇔

68° ✓

$d$

⇔

90° ✓
What is the area of this rhombus?

30 cm²

40 cm²

48 cm² ✓

240 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)?

'1440' ✓
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)?

'240' ✓

Exit quiz

Which of these diagrams show a perpendicular bisector on a rhombus?

a

b ✓

c

d ✓

e
Which of these compass widths are suitable when constructing the perpendicular bisector of the given line segment?

a

b ✓

c ✓
Which of these constructions can be used to draw on the perpendicular bisector of the line segment given?

a ✓

b

c

d ✓

e
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.

point A

⇔

7 cm away from Y and greater than 7 cm away from Z. ✓

point B

⇔

7 cm away from Y and less than 7 cm away from Z. ✓

point C

⇔

7 cm away from Z and greater than 7 cm away from Y. ✓

point D

⇔

7 cm away from both Y and Z. ✓
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.

Constructing arcs of radius 12 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.
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.

The construction of the perpendicular bisector to YZ is incomplete. ✓

The angle between the two line segments is 88°.

Two more arcs need to be constructed. ✓

Worksheet

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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.

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.

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.