CAIE IGCSE Mathematics Extended 4 Geometry Topic Practice

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Covered syllabus points

E4.1 Geometrical termsE4.2 Geometrical constructionsE4.3 Scale drawingsE4.4 SimilarityE4.5 SymmetryE4.6 AnglesE4.7 Circle theorems IE4.8 Circle theorems II

Question 1

[Maximum number: 7]

Question (a)

(a)
Figure for Question (a) — CAIE IGCSE Mathematics Extended

NOT TO
SCALE
ABCDEF is a regular hexagon.
D F, D A and DB are diagonals.
Complete the following statements using three different triangles.
Triangle DEF is congruent to triangle ......
Triangle ...... is congruent to triangle ......

[ 2 ]

Question (b)

(b)
Figure for Question (b) — CAIE IGCSE Mathematics Extended

NOT TO SCALE
P and Q are points on the circle with centre O.
TP and TQ are tangents to the circle from the point T.
Complete the following statements and reasons.
In triangles OPT and OQT
O P= ...... because each is a radius of the circle
OT is a common side

Angle O P T= angle ...... =90^ because ......
Triangles OPT and OQT are congruent using the criterion ......
This proves that the tangents TP and TQ are ......

[ 5 ]

Question 2

[Maximum number: 1]
Figure for Question 2 — CAIE IGCSE Mathematics Extended

Measure the marked angle.

Question 3

[Maximum number: 3]

A lake has an area of 3 km23 \mathrm{~km}^{2}.
On a map the area of the lake is 18.75 cm218.75 \mathrm{~cm}^{2}.
Find the scale of the map in the form 1: n.

Question 4

[Maximum number: 5]
NOT TO SCALE

NOT TO SCALE

The diagram shows a cyclic quadrilateral ABCD. BD and AC intersect at X.

Question (a)

(a)

Angle BAD=74∘B A D=74^{\circ} and angle BCA=34∘B C A=34^{\circ}.

Find

[ 3 ]

Question (i)

(i)

angle BDA

Angle B D A=

[ 1 ]

Question (ii)

(ii)

angle BCD

Angle B C D=

[ 1 ]

Question (iii)

(iii)

angle ABD.

Angle A B D=

[ 1 ]

Question (b)

(b)

In the diagram, triangle ADX is similar to triangle BCX.
BC=4.5 cm,AD=9 cmB C=4.5 \mathrm{~cm}, A D=9 \mathrm{~cm} and CX=3.3 cmC X=3.3 \mathrm{~cm}.

Work out XD.
X D= cm [2]

[ 2 ]
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