CAIE IGCSE Mathematics Extended E4.4.3 Solve Problems and Give Simple Explanations Involving Similarity Questions

Practise Extended CAIE IGCSE Mathematics by setting up proportions and explaining results for similar figures.

Exam points

Use similarity to solve geometric problems involving corresponding lengths and areas.
Set up and solve proportions between similar figures.
Give a concise explanation showing how similarity supports the result.

[Maximum number: 4]

NOT TO SCALE

G, K and M lie on a circle, centre O.
FGH is a tangent to the circle at G and MG is parallel to OH.
Show that triangle GKM is mathematically similar to triangle OHG.
Give a geometrical reason for each statement you make.

Two pairs of equal angles identified with fully correct reasons
M3
M2 for one pair of equal angles identified with fully correct reasons
Examples:
$KMG=90^\circ$ (angle in semicircle) and $OGH=90^\circ$ (angle between tangent and radius)
OR KMG=OGH (alternate segment)
OR GOH=MGK (alternate angles)
OR angle FGM= angle GHO (corresponding), angle FGM=GKM (alternate segment), and angle H= angle K
M1 for $KMG=90^\circ$ angle in semicircle or $OGH=90^\circ$ angle between tangent and radius
A1 dep on M3 with no incorrect work: two or three pairs of angles equal, so triangles are similar

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CAIE IGCSE Mathematics Extended E4.4.3 Solve Problems and Give Simple Explanations Involving Similarity Questions question 1