Properties of triangles & quadrilaterals

Points A, B and C are plotted on a grid.

Write down the coordinates of C.

Write down the coordinates of the midpoint of AC.

Plot point D on the grid so that ABCD is a rhombus.

AB is a straight line.

Work out the size of angle x.

Work out the size of angle y.

Three straight lines intersect as shown.

What type of triangle is made? You must show your working.

Write down the name of a triangle with three equal sides.

Write down the name for the straight line inside this circle.

A (1, 3) and B (2, 9) are points on a centimetre grid.

ABCD is a parallelogram. AD and BC are horizontal and each has length 5 cm The diagonals of ABCD cross at E. Work out the two possible pairs of coordinates of E.

A diagonal of a rectangle is drawn on a centimetre grid. The sides of the rectangle are on the grid lines.

Work out the area of the rectangle.

One side of a parallelogram is drawn on this centimetre grid. The parallelogram does not have any right angles. Complete the parallelogram so that it has area 24 cm²

Two sides of a rhombus are drawn on this grid. Complete the rhombus.

Quadrilateral ABCD has

• angle ABC = 90°

• CD is parallel to BA

Draw ABCD on the centimetre grid. AB has been drawn for you.

Lines AB and BC are shown.

Write down the coordinates of C.

Write down the coordinates of the midpoint of AB.

D is the point on the grid that makes ABCD a parallelogram. Work out the coordinates of D.

Write down the equation of the line passing through A and B.

A quadrilateral has angles 70 °, 110 °, 130 ° and 50 ° Circle the possible type of quadrilateral.

kite parallelogram rhombus trapezium

Which shape can have sides with lengths that are all different? Circle your answer.

trapezium kite parallelogram rhombus

Here is a parallelogram.

Circle the expression for the perimeter.

2 s + 2 w s + w sw 2 sw

A, B and C are three points on the circumference of a circle, centre O. BD and CD are tangents to the circle. ABDC is a kite.

Prove that angle ABO is 45° –

A rhombus is cut along the diagonals to make four triangles.

Which three statements are correct for any rhombus? Tick three boxes.

Five points are plotted on a centimetre grid.

The points are five of the vertices of a hexagon. Each side of the hexagon has the same length. Work out one possible pair of coordinates of the other vertex.

Here is a triangle on a square dotty grid.

On the grid below, show how you can make a parallelogram with two of these triangles.

On the grid below, show how you can make a trapezium with three of these triangles.

On the grid below, show how you can make a rhombus with four of these triangles.

Here is a quadrilateral.

a = 90° and a: b = 5: 3 x: y = 1: 3 Show that b = x

The diagram shows rectangle ABDE and right-angled triangle ABC. AC = 17 cm BC = 8 cm

BC: CD = 1: 2 Work out the area of rectangle ABDE.

Which shape must have rotational symmetry? Circle your answer.

isosceles triangle trapezium kite parallelogram

Two sides of a triangle have lengths 13 cm and 27 cm

Which of these is a possible length of the other side? Circle your answer.

13 cm 14 cm 27 cm 40 cm

Trapezium ABCE is made from parallelogram ABCD and isosceles triangle ADE.

Work out the size of angle AED.

Here are five shapes, A to E.

In the Venn diagram, ξ is the set of all shapes Q is the set of quadrilaterals R is the set of shapes which always have rotational symmetry.

Complete the Venn diagram with the letters A to E.

A large rectangle is made by joining three identical small rectangles as shown.

The perimeter of one small rectangle is 15 cm Work out the perimeter of the large rectangle.

BCD is a straight line. Triangle ABC is equilateral. CE = DE

Work out the size of angle x.

Amba is working out the size of an interior angle of a regular octagon.

Her method is Interior angle = 360 ÷ 8 Is her method correct?

Give a reason for your answer.

Tick all the statements that are true for any rhombus.

Which of these shapes has two lines of symmetry? Circle your answer.

Semicircle Rhombus Trapezium Isosceles triangle

ABCDE is a pentagon.

Show that BCDE is a parallelogram.

ABCD is a parallelogram.

Work out the size of angle x.

ABCD is a parallelogram. AB = BP

Work out the size of angle x.

This shape is made from two triangles and four congruent parallelograms.

For each statement, tick the correct box.

The triangles are equilateral.

The triangles are congruent.

This shape is made from two triangles and four congruent parallelograms.

For each statement, tick the correct box.

The triangles are equilateral.

The triangles are congruent.