Edexcel IGCSE Maths
Topic questions Geometry and measures Geometric reasoning & proof
25 questions · 109 marks · about 2 hours
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.
ABCD is a quadrilateral.
ADE is a straight line.
Work out the value of x Give a reason for each stage of your working.
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
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
A, B, C and D are points on a circle, centre O
Angle BCD = 128°
Work out the size of angle OBD Give a reason for each stage of your working.
angle = OBD........
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.
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.
Also involves Angle facts
P, Q, R and S are points on a circle with centre O
PS is a diameter of the circle.
Angle PQR = 136
Work out the size of angle RPS
ABC is a straight line and BCD is a triangle.
Work out the value of x
PO, RO, SO and TO are four straight lines.
Work out the value of y
Give a reason for your answer.
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 10-sided polygon, ABCDEFGHIJ
Show that x = y
Also involves Angle facts
D, E, F and G are points on a circle, centre O
EOG is a diameter of the circle.
Angle EGD = 42°
Calculate the size of angle DFG Give a reason for each stage of your working.
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.
B, D, E and F are points on a circle.
ABC is the tangent at B to the circle. Angle ABD = 39
Angle EFD = 18
Work out the size of angle BDE. Give reasons for your working.
Also involves Tangent to a circle
B, D, E and F are points on a circle. ABC is the tangent to the circle at B.
Angle EDF = 40
Angle FBC = 70
Prove that the tangent ABC is parallel to EF. Give a reason for each stage of your working.
The diagram shows a trapezium ABCD in which AB and DC are parallel.
AB = DB
Work out the value of x. 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.
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.
A, B and C are points on a circle, centre O. Angle ABC = 38°
Work out the size of angle OAC. Give a reason for each stage of your working.
ABC is a triangle. D and E are points such that ACD and BCE are straight lines.
reflex angle ABC = 298° angle ECD = 97°
Work out the size of angle x. Give a reason for each stage of your working.
Also involves Tangent to a circle
A, B, C and D are points on a circle. TDV is the tangent to the circle at D.
AB = AD Angle ADT = 71°
Work out the size of angle BCD. Give a reason for each stage of your working.
Also involves Angle facts
B, C, D and F are points on a circle. ABC, AFD, BFE and CDE are straight lines.
Work out the size of angle x. Show your working clearly.
Also involves Tangent to a circle
L, M and N are points on a circle, centre O. QMT is the tangent to the circle at M.
Find the size of angle NOM.
Give a reason for your answer.
Find the size of angle NMQ.
Give a reason for your answer.
Also involves Properties of triangles and quadrilaterals
The diagram shows a hexagon ABCDEF. BC is parallel to ED.
Work out the size of the obtuse angle DEF.
Memes
Laugh now. Cry in the exam hall later. Then come back and do a past paper.
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