EduNinja

[Maximum number: 7]

NOT TO SCALE

In the diagram, S lies on PQ and T lies on PR.
ST is parallel to QR.

(a)

Explain why triangle PQR is mathematically similar to triangle PST.

Give a geometrical reason for each statement you make.

[ 3 ]

Three correct pairs with correct reasons

$\angle PQR=\angle PST$ and corresponding angles
$\angle PRQ=\angle PTS$ and corresponding angles
$\angle QPR=\angle TPS$ and common angle
OR
Two correct pairs with correct reasons and correct similarity condition, e.g. AAA

B2 for two correct pairs with correct reasons
or B1 for one correct pair with correct reason

(b)

$S T=3 \mathrm{~cm}, Q R=9 \mathrm{~cm}$ and $P S=5 \mathrm{~cm}$ .

Work out PQ.

[ 2 ]

15

M1 for $\frac39=\frac5{PQ}$ oe or better

(c)

The area of triangle PST is $2 k \mathrm{~cm}^{2}$ .

Find, in terms of k, the area of quadrilateral QRTS. $\mathrm{cm}^{2}$

[ 2 ]

16k

M1 for $3^2$ or $(\frac13)^2$ oe

[Maximum number: 3]

A sector of a circle has radius 8 cm and area 160 cm^2.

A mathematically similar sector has radius 20 cm .
Calculate the area of the larger sector.
cm^2
[3]

1000 cao
M2 for $160\times\left(\frac{20}{8}\right)^2$ or $160\div\left(\frac{8}{20}\right)^2$ oe
or M1 for $\left(\frac{20}{8}\right)^2$ or $\left(\frac{8}{20}\right)^2$ oe

CAIE IGCSE Mathematics Extended E4.4 Similarity Topic Practice

Question 1

Question (a)

Question (b)

Question (c)

Question 2