Edexcel IGCSE Maths
Topic questions Geometry and measures Properties of triangles & quadrilaterals
81 questions · 339 marks · about 7 hours
The diagram shows a 6-sided polygon.
Measure the length of the side AB Give the units of your answer.
Measure the size of the angle marked x
Write down the mathematical name of a 6-sided polygon.
AEC and BED are straight lines.
Sergio says that the value of x is 58
Give a reason why Sergio is correct.
In the diagram, GHIJ is a quadrilateral.
Chloe says “FGH is a straight line”
Show that Chloe is wrong. Give a reason for each stage of your working.
AB and BC are two sides of a regular polygon with n sides.
Work out the value of n Show your working clearly.
AB and BC are two sides of a regular polygon with n sides.
Work out the value of n Show your working clearly.
The diagram shows a quadrilateral ACDF
ABEF is a trapezium.
BCDE is a parallelogram.
FE = 26 cm AB = 18 cm BC = 12 cm
The area of the parallelogram BCDE is 96 cm2
Work out the area of the trapezium ABEF
Here are two shapes.
Write down the mathematical name of the
triangle,
quadrilateral.
On the triangle, draw the line of symmetry.
Write down the order of rotational symmetry of the quadrilateral.
ABCD is a quadrilateral.
ADE is a straight line.
Work out the value of x Give a reason for each stage of your working.
Here is a polygon.
Write down the mathematical name of this polygon.
Write down the number marked with the arrow.
Here are four clock faces.
Write down the letter of the clock face that shows quarter to five.
Complete the following sentence by writing a suitable metric unit on the dotted line.
The height of the Eiffel Tower is 300........
Work out the value of x
Give a reason for your answer.
ABDE is a quadrilateral. BCD is an isosceles triangle. ABC is a straight line.
Work out the value of y
The diagram shows three points, A, B and C, marked on a grid.
Write down the coordinates of A
Find the coordinates of the midpoint of AB
D is the point on the grid so that ABCD is a rectangle.
Find the coordinates of D
ABCD is a quadrilateral. CDE is an isosceles triangle with CD = CE DEF is a straight line.
Work out the size of angle BCE Give a reason for each stage of your working.
angle = BCE........
Also involves Angle facts
In the diagram, ABCDE is a regular pentagon.
Angle AEF = 96°
Work out the size of the obtuse angle FED Show your working clearly.
Also involves Angle facts
In the diagram, ABCDE is a regular pentagon.
Angle AEF = 96°
Work out the size of the obtuse angle FED Show your working clearly.
24A polygon has n sides, where n 
5
The interior angles of the polygon form an arithmetic sequence.
The smallest angle of the polygon is 84° The common difference of the sequence is 4°
Work out the sum of the interior angles of the polygon. Show clear algebraic working.
Here is a quadrilateral.
What is the mathematical name for this type of quadrilateral?
The diagram shows a 3-D shape.
What is the mathematical name for this 3-D shape?
How many edges has this shape?
The size of each exterior angle of a regular polygon is 15°
Work out the number of sides of the regular polygon.
The diagram shows a 5-sided polygon, ABCDE
Write down the mathematical name for a 5-sided polygon.
Measure the length of the line AB Give your answer in centimetres.
On the diagram, mark an obtuse angle with the letter T
Also involves Geometric reasoning and proof
The diagram shows quadrilateral ABCD
ECD, BCF and GAD are straight lines.
Work out the value of x Give a reason for each stage of your working.
Also involves Angle facts
BCDEFG is a hexagon. AB, BC and CD are three sides of a regular n‑sided polygon.
Calculate the value of n Show your working clearly.
The diagram shows two circles with centre O and a regular pentagon ABCDE
A, B, C, D and E are points on the larger circle. The pentagon has sides of length 8 cm.
The diagram is shaded such that
shaded area = unshaded area
Work out the radius of the smaller circle. Give your answer correct to 3 significant figures.
The diagram shows three points, A, B and C, marked on a grid.
Write down the coordinates of point A
On the grid, mark with a cross (
) the point D so that ABCD is a rectangle.
Find the coordinates of the midpoint of AC
On the grid, draw the line with equation y = 4
Write down the mathematical name of this polygon.
Measure the length of the line AB Give your answer in centimetres.
Here are six triangles drawn on a grid of squares.
Two of these triangles are congruent.
Write down the letters of these two triangles.
ABCD is a trapezium.
BC is parallel to AD
Find the size of the largest angle inside the trapezium.
Also involves Angle facts
Here is a 9-sided regular polygon ABCDEFGHJ, with centre O
ODK and FEK are straight lines.
Work out the value of x
Also involves Angle facts
ABCD is a trapezium.
BC is parallel to AD
Find the size of the largest angle inside the trapezium.
Also involves Angle facts
Here is a 9-sided regular polygon ABCDEFGHJ, with centre O
ODK and FEK are straight lines.
Work out the value of x
Also involves Coordinate geometry
ABCD is a kite with AB = AD and CB = CD
A is the point with coordinates (–2, 10)
Work out the coordinates of D
BCD is an isosceles triangle with BD = CD ABC is a straight line. ABDE is a quadrilateral.
Work out the value of x Give a reason for each stage of your working.
The diagram shows a pentagon.
Work out the value of x
The diagram shows a pentagon.
Work out the value of x
Also involves Coordinate geometry
ABCD is a kite.
AB = AD and CB = CD
The point B has coordinates (k, 1) where k is a negative constant. The point D has coordinates (8, 7)
The straight line L passes through the points B and D
The straight line L is parallel to the line with equation 5y – 3x = 6
Find an equation of AC Give your answer in the form px + qy = r where p, q and r are integers. Show your working clearly.
Write down the mathematical name for an 8-sided polygon.
What type of angle is the angle marked x?
On the diagram above, draw a chord of the circle.
Change 3.6 metres into centimetres.
AB, BC, CD, DE and EF are five sides of a regular polygon.
RST, SCU and BCV are straight lines. RST is parallel to CD Angle RSC = 128° Angle UCV = 32°
Work out how many sides the polygon has. Show your working clearly.
AB, BC, CD, DE and EF are five sides of a regular polygon.
RST, SCU and BCV are straight lines. RST is parallel to CD Angle RSC = 128° Angle UCV = 32°
Work out how many sides the polygon has. Show your working clearly.
ABCD is a trapezium with AB parallel to DC
A is the point with coordinates (–4, 6) B is the point with coordinates (2, 3) D is the point with coordinates (–1, 8)
The trapezium has one line of symmetry. The line of symmetry intersects CD at the point E
Work out the coordinates of the point E
Here is a polygon.
Write down the mathematical name of this polygon.
Here is a scale.
On the scale, mark with an arrow (↑) the number 360
Here is a clock face.
Write down the time shown on the clock face.
Complete the following sentence by writing a suitable metric unit on the dotted line.
ABC is a straight line.
Work out the value of x
Give a reason for your answer to (i)
CDE is an equilateral triangle. ABCF is a quadrilateral.
BCE and DCF are straight lines.
Work out the value of y You must show your working.
Also involves Angle facts
The diagram shows parts of three regular polygons, A, B and C, meeting at a point.
Polygon B has n sides.
Work out the value of n.
Also involves Angle facts
The diagram shows parts of three regular polygons, A, B and C, meeting at a point.
Polygon B has n sides.
Work out the value of n.
Also involves Forming and solving equations
23A polygon has n sides, where n 
5
When arranged in order of size, starting with the largest number, the sizes of the interior angles of the polygon, in degrees, are the terms of an arithmetic sequence.
Here are the first five terms of this sequence.
177 175 173 171 169
Find the value of n Show clear algebraic working.
Here are two sides of a parallelogram.
On the grid above, complete the parallelogram.
The diagram shows a 3‑D shape.
What is the mathematical name of this 3‑D shape?
How many faces has this shape?
Also involves Trigonometry
The diagram shows triangle ABP inside the regular hexagon ABCDEF
AB = 5 cm BP = 2 cm Angle ABP = 90
Work out the size of angle PAF Give your answer correct to 3 significant figures.
The diagram shows triangle ABP inside the regular hexagon ABCDEF
AB = 5 cm BP = 2 cm Angle ABP = 90
Work out the size of angle PAF Give your answer correct to 3 significant figures.
Here are three shapes.
A B C
Shape A is a triangle.
Write down the mathematical name for this type of triangle.
Shape B is a rectangle.
On shape B, draw its lines of symmetry.
Shape C is a regular polygon.
Write down the order of rotational symmetry of shape C.
Also involves Parallel and perpendicular lines
The diagram shows a 5‑sided polygon.
Measure the length of the side AB Give the units of your answer.
Measure the size of the angle marked x
On the diagram, mark with arrows (
) a pair of parallel sides.
Write down the mathematical name of a 5‑sided polygon.
The diagram shows three points, A, B and C, on a grid.
Write down the coordinates of
point A
point B
D is the point such that ABCD is a rhombus.
On the grid, mark with a cross (
) the point D Label this point D
Find the coordinates of the midpoint of AB
Here is a quadrilateral.
Work out the value of x
Give a reason for your answer.
Also involves Angle facts
The diagram shows a regular octagon ABCDEFGH and a regular pentagon ABIJK
Work out the size of the angle x
Also involves Angle facts
The diagram shows a regular octagon ABCDEFGH and a regular pentagon ABIJK
Work out the size of the angle x
Also involves Angle facts
The diagram shows a regular 10-sided polygon, ABCDEFGHIJ
Show that x = y
Also involves Area and perimeter
Here are five fractions.
Two of the fractions in the table are equivalent to 
Put a tick () in the box underneath each of these two fractions.
The diagram shows an 8-sided polygon and its diagonals.
Write down the mathematical name of an 8-sided polygon.
Shade 
of the polygon shown in the diagram above.
The area of a polygon is 56 cm2
Here is a quadrilateral.
What is the mathematical name of this quadrilateral?
Measure the size of the angle marked x.
On the quadrilateral, mark with arrows (
) a pair of parallel lines.
The quadrilateral has four angles.
How many of these angles are right angles?
The diagram shows quadrilateral ABCD and isosceles triangle ADE, where AE = AD.
EDC is a straight line.
Work out the value of x. Give a reason for each stage of your working.
The diagram shows a regular pentagon, ABCDE, a regular hexagon, CFGHID, and a quadrilateral, EDIJ.
AEJ and HIJ are straight lines.
Work out the size of the angle marked x. Show your working clearly.
The diagram shows a regular pentagon, ABCDE, a regular hexagon, CFGHID, and a quadrilateral, EDIJ.
AEJ and HIJ are straight lines.
Work out the size of the angle marked x. Show your working clearly.
The diagram shows five shaded shapes on a grid of squares.
Two of the shapes are congruent.
Write down the letters of these shapes.
On the square grid below, draw a shape that is similar to but is not congruent to shape B.
All of the shapes on the grid have 6 sides.
Write down the mathematical name for a shape that has 6 sides.
Here is a polygon with five sides.
Write down the mathematical name of a polygon with five sides.
Measure the size of the angle marked x.
Two sides of the polygon are parallel.
On the polygon, mark with arrows (>>) this pair of parallel lines.
Here are two triangles.
Triangle A
Triangle B
Are triangle A and triangle B similar triangles? You must give a reason for your answer.
Also involves Forming and solving equations
Here is a 10-sided polygon.
Work out the value of x.
The diagram shows a regular octagon ABCDEFGH.
Work out the size of angle HAC.
Also involves Linear equations
Here is a 10-sided polygon.
Work out the value of x.
The diagram shows a regular octagon ABCDEFGH.
Each side of the octagon has length 10 cm.
Find the area of the shaded region ACDEH. Give your answer correct to the nearest cm2
Also involves Coordinate geometry
ABCD is a rhombus.
The diagonals, AC and BD, intersect at the point M. The coordinates of M are (6, −11)
The points A and C both lie on the line with equation 2y + 7x = 20
Find the exact coordinates of the point where the line through B and D intersects the y-axis.
The diagram shows a quadrilateral ABCD drawn on a square grid.
Measure the length of BC.
Write down the mathematical name of quadrilateral ABCD.
Write down the order of rotational symmetry of quadrilateral ABCD.
On the diagram, mark an obtuse angle with the letter x.
Here is a diagram of a trapezium.
Work out the area of the trapezium.
The diagram shows a parallelogram ABCD and an isosceles triangle DEF in which DE = DF
CDF and ADE are straight lines. Angle BCD = 58°
Work out the size of angle DEF. Give a reason for each stage of your working.
The diagram shows a parallelogram ABCD and an isosceles triangle DEF in which DE = DF
CDF and ADE are straight lines. Angle BCD = 58°
Work out the size of angle DEF. Give a reason for each stage of your working.
On the grid below, draw a kite.
Write down the mathematical name of an 8-sided polygon.
Here is a solid prism.
Write down the mathematical name of this prism.
How many vertices does the prism have?
ABDE is a quadrilateral. ABC is a triangle. DCB is a straight line.
Work out the value of x.
Give a reason for your answer.
Work out the value of y. Give a reason for each stage of your working.
Also involves Forming and solving equations
The diagram shows a regular hexagon, ABCDEF, and an isosceles triangle, GHJ.
The perimeter of the hexagon is equal to the perimeter of the triangle.
Find the length of each side of the hexagon. Show clear algebraic working.
P, Q and R are three points marked on a grid.
Write down the coordinates of point Q.
S is the point such that PQRS is a rectangle.
Find the coordinates of point S.
Find the coordinates of the midpoint of PR.
Also involves Forming and solving equations
A regular polygon has n sides. The size of each interior angle of the regular polygon is 140°
Work out the value of n.
The diagram shows two congruent isosceles triangles and parts of two congruent regular polygons, X and Y.
The two regular polygons each have n sides.
Work out the value of n.
The diagram shows two congruent isosceles triangles and parts of two congruent regular polygons, X and Y.
The two regular polygons each have n sides.
Work out the value of n.
Complete the following statements by writing a number on each dotted line.
A pentagon has........ sides.
The size of each angle in an equilateral triangle is........ °
1 kilometre =........ metres.
Each exterior angle of a regular polygon is 24°
Work out the number of sides of the polygon.
Each interior angle of a regular polygon is 162°
Work out the number of sides the polygon has.
ABCD is a kite with AB = AD and CB = CD.
B is the point with coordinates (10, 19) D is the point with coordinates (2, 7)
Find an equation of the line AC. Give your answer in the form py + qx = U where p, q and U are integers.
ABCD is a quadrilateral. ADE is an equilateral triangle. DCF is a straight line.
Work out the size of angle EAB. Give a reason for each stage of your working.
Also involves Measuring lengths and angles, bearings
The diagram shows points A, B and C on a square grid.
Write down the coordinates of C.
Measure the length of BC. Give your answer in centimetres.
On the grid, mark with a cross (X) the point D so that ABCD is a parallelogram. Label this point D.
BCDE is a rectangle. ABE is an isosceles triangle.
AB = AE Angle BAE = 80
Work out the size of angle x.
The diagram shows a regular pentagon, ABCDE, a regular octagon, ABFGHIJK, and an isosceles triangle, BCF.
Work out the size of angle x.
The diagram shows a regular pentagon, ABCDE, a regular octagon, ABFGHIJK, and an isosceles triangle, BCF.
Work out the size of angle x.
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