Constructing rhombi

Maths

Checking compass skills

Securing the skill of using a pair of compasses

Understanding constructing a circle

Constructing triangles

Diagonals of a rhombus

Bisecting an angle

Perpendicular bisector of a line segment

Perpendicular to a given line through a given point

Problem solving with constructions

The constructions covered in this unit are built on in the future unit. In the future unit, pupils construct triangles and construct diagrams following specific restrictions.

The prior unit gave pupils the opportunity to explore polygons and begin to generalise their understanding of interior/exterior angles in regular polygons. In this unit, pupils will use the geometrical properties of a rhombus to perform various constructions. 

In this unit we develop skills in using a pair of compasses and ruler to construct various accurate shapes and angles including triangles, rhombi, perpendicular lines and angle bisectors.

Constructions

This kite has be created by using two triangles, joined by a common edge length. The two triangles are ...

A rhombus is a {{ }} where all sides are the same length.

Which of these show the correct construction of a rhombus?

Yes - both of the rhombi would have edge lengths of 8 cm, so they are the same.

No - they can have the same edges but the angles can be different.

Maybe - if they both constructed the rhombus using equilateral triangles.

If Jun and Jacob were to both construct a rhombus with edge lengths of 8 cm, would their constructions be identical?

Sofia is constructing a rhombus from one given edge AB. She has nearly finished the construction of rhombus ABCD. Where is vertex D?

{{ }} triangles have two equal-sized angles. Two of the three edges are equal in length. 

As this triangle is isosceles, the angle marked $$a$$ is {{ }}$$^\circ$$.

Which of these could be a sketch of an equilateral triangle?

Which of the following sets of lengths could be the edges of a triangle?

Interior angles of all quadrilaterals sum to $$180^\circ$$.

All quadrilaterals have at least one set of parallel sides.

All quadrilaterals can be split into two triangles.

Select all the statements which are true of all quadrilaterals.

Use your pencil and ruler to draw one edge to the required length.

Set the width of the pair of compasses to the length of the drawn edge. 

With the needle point on one end of the line segment, draw an arc.

Put the needle point on the other end of the line segment.

Check the width of the pair of compasses is still the length of the edge.

Draw an arc, which intersects with the first arc.

Connect the point of intersection to the ends of the line segment.

Put the steps of constructing an equilateral triangle in order.

Constructing rhombi

Lesson outcome