Similarity

The figure shows triangle $ABC$ and triangle $XYZ$ are similar. The side lengths are $AB=3$ cm, $BC=8$ cm, $YZ=12$ cm and $ZX=15$ cm.

May/June 2015

ANB, BLC and CMA are straight lines. $NM$ runs parallel to $BC$, and $LN$ runs parallel to $CA$.

May/June 2016

The diagram depicts triangle $ABC$. Point $D$ lies on $AC$ so that $\angle BDC = \angle ABC$.

May/June 2019

The figure $ACD$ forms a triangle with $\angle ADC = 110^\circ$. Also, $EB$ is parallel to $DC$, and $AE = EB$.

May/June 2019

Points P, Q and R lie on the circumference of a circle with centre $O$. The angle $POQ$ is $8x^{\circ}$, the angle $RPO$ is $x^{\circ}$ and the angle $OQR$ is $24^{\circ}$.

May/June 2021

Rectangle $ABCD$ is similar to rectangle $PQRS$. The measurements are $AB = 12\text{ cm}$, $BC = 9\text{ cm}$ and $PQ = 8\text{ cm}$.

May/June 2023

Prism $A$ is mathematically similar to prism $B$. In the diagram, the shaded regions show the cross-sections of the prisms. The volume of prism $A$ is $5000\,\text{cm}^3$. The length of prism $A$ is $50\,\text{cm}$. The area of the cross-section of prism $B$ is $16\,\text{cm}^2$.

May/June 2024

Triangles $ABC$ and $CBD$ are mathematically similar. $AB = 5\text{ cm}$, $AC = 7\text{ cm}$ and $BC = 8\text{ cm}$.

May/June 2024

Triangle $PQR$ is isosceles because $PQ = QR$. The exterior angle at $R$ is $142^\circ$. Calculate angle $PQR$.

May/June 2024

From the diagram, triangles $APQ$ and $ABC$ are similar. Since $BC$ is parallel to $PQ$, and $AP = 4$ cm, $PB = 2$ cm and $PQ = 1.8$ cm.

Oct/Nov 2016

The diagram displays two circles, each with centre $O$.

Oct/Nov 2017

The diagram contains two circles that touch at $C$. $A$, $B$ and $C$ lie on the smaller circle, whose centre is $X$. $C$, $D$ and $E$ lie on the larger circle, whose centre is $Y$. $AXCYE$ and $BCD$ are straight lines, and $Y\hat{D}E = x^\circ$.

Oct/Nov 2018

Angles in polygons together with similar triangles.

Oct/Nov 2020

The diagram shows that $ACD$ and $BCE$ are straight lines, with $AB$ parallel to $ED$.

Oct/Nov 2021

In the diagram, rectangle $ABCD$ is shown. Point $E$ lies on the diagonal $AC$ so that $\angle DEC = 90^\circ$.

Oct/Nov 2021

Triangle $ABC$ is similar in the mathematical sense to triangle $DEC$. $AB = 12\,\text{cm}$, $BC = 27\,\text{cm}$, $CD = 7\,\text{cm}$ and $DE = 3\,\text{cm}$.

Oct/Nov 2022

The diagram depicts two mugs that are mathematically similar. The smaller mug has width $w$ cm and, when full, contains $270$ ml. The larger mug has width $8$ cm and, when full, contains $640$ ml.

Oct/Nov 2024

A, D and B lie on the same straight line, and A, E and C lie on another straight line. BC is parallel to DE. BC = $9.8\,\text{cm}$, BD = $2.7\,\text{cm}$, DE = $5.6\,\text{cm}$ and CE = $3.9\,\text{cm}$.

Oct/Nov 2024

The diagram depicts a prism whose cross-section is an isosceles triangle with side lengths 13 cm, 13 cm and base 10 cm. The prism has length 3 cm.

Oct/Nov 2025

Triangles ABC and PQR are similar. In triangle ABC, AB = 6 cm and AC = 7 cm, while in triangle PQR, PQ = 9 cm.

Oct/Nov 2025

$ABCD$ forms a parallelogram. $E$ lies on $AB$ and $EC=BC$. Angle $ECB=40\degree$ and angle $DEC=60\degree$.

Oct/Nov 2025