# Form 2 Mathematics Topical Questions and Answers on Similarity and Congruence

Form 2 Mathematics Questions and Answers on Similarity and Congruence. Similarity and Congruence is a subtopic under transformations, a form 2 topic. Answers are in video format.

Lessons (**17**) * SHARE*

- 1.
In the figure below, ABCD is a cyclic quadrilateral and BC is parallelto AD. Show that triangle ABX is congruent to triangle DXC

5m 39s - 2.
In the triangle ABC shown below, DE is parallel to BC. If AE=3cm and EC=2cm, determine the ratio of the area of the triangle ADE to that of triangle ABC.

3m 11s - 3.
In the figure below AD//BC. AC and BD intersect at E. given that AE: EC=1:5 and BD=12cm, calculate the length of DE.

4m 46s - 4.
In the figure below, triangle ABC is similar to triangle AED and BC//ED. Given that the ratio AB: AE=2:5, find the ratio of the area of triangle ABC to that of the trapezium BCDE.

3m 46s - 5.
In the figure given below (not drawn to scale) DC is a tangent to the circle centre O. AOBC is a straight line. (a) Show that triangle ADC is similar to triangle DBC. (b) Given that BC=4cm and DC=6cm, calculate: i).the length of AB. ii) the size of angle ACD.

9m 19s - 6.
In the figure below, the chord AB and CD intersect at E. show that triangle AED is similar to triangle BEC.

3m 48s - 7.
In the triangle ABC below, AC=8cm, BC=5cm and angle BCA=#30^0#. Point D divides BC in the ratio 1:4 and point E divides AC in the ratio 2:3. Find the area of the quadrilateral ABDE.

5m 12s - 8.
A football tube in the form of a sphere is inflated so that its radius increases in the ratio of 4:3. Find the ratio in which the volume is increased

1m 12s - 9.
A container of height 30cm has a capacity of 1.5 litres. What is the height of a similar container of capacity #3.0 m^3#

3m 52s - 10.
The ratio of the lengths of the corresponding sides of the two similar rectangular water tanks is 3:5. The volume of the smaller tank is #8.1 m^3#. Calculate the volume of the larger tank.

1m 47s - 11.
Pieces of soap are packed in a cuboid container measuring 36cm by 24 cm by 18 cm. each piece of soap is similar to the container. If the linear scale factor between the container and the soap is #1/6# , find the volume of each piece of soap.

2m 21s - 12.
In the diagram below, ABCD is trapezium with AB parallel to DC. The diagonals AC and BD intersect at E. (a). giving reasons show that triangle ABE is similar to triangle CDE (b). given that AB=3DC, find the ratio of DB to EB.

6m 53s - 13.
The volumes of two similar solid cylinders are #4752cm^3# and #1408 cm^3# if the area of the curved surface of the smaller cylinder is #352 cm^2# , find the area of the curved surface of the larger cylinder.

2m 55s - 14.
In the figure below, angles BAC and ADC are equal. Angle ACD is a right angle. The ratio of the sides AC:BC=4:3. Given that the area of triangle ABC is #24cm^2#, find the area of triangle ACD.

2m 57s - 15.
A glass in form of a frustum of a cone, is represented by the diagram below. The glass contains water to a height of 9cm. the bottom of the glass is a circle of radius 2 cm while the surface of the water is a circle of the radius 6 cm. (a). calculate the volume of the water in the glass (b). when a spherical marble is sub-merged into the water in the glass, water level rises by 1 cm. calculate:

12m 39s - 16.
A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16cm. if the volume of the smaller cone is #160cm^3#, find the volume of the frustum.

4m 39s - 17.
The diagram below represents a cone of height 12cm and a base radius of 9cm from which a similar smaller cone is removed, leaving a conical hole of height 4 cm. (a). calculate: (i) the base radius of conical hole. (ii). The volume, terms of ?, of the smaller cone that was removed. (b) (i) determine slant height of the original cone.

8m 20s

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