ICSE Class 8 Maths Geometry Unit Test Paper

Unit Test Paper

Geometry

Question 1

Find the measure of x in the following figures.

(i) The figure shows angles formed by intersecting lines with expressions: \(3x + 6\), \(2x - 7\), and \(\frac{7x}{2}\).

(ii) The figure shows angles with expressions: \(x + 12\), \(x - 12\), and \(\frac{10x}{13}\).

(iii) The figure shows angles with expressions: \(5x - 25\) and \(x\).

(iv) The figure shows angles with expressions: \(2x\) and \(7x - 3\).

(v) The figure shows angles with expressions: \(23x\), \(17x\), and \(30x\).

(vi) The figure shows angles with expressions: \(x\), \(101°\), and \(28°\).

(vii) The figure shows angles with expressions: \(x + 10\), \(\frac{x}{2} - 10\), \(135°\), and \(\frac{x}{2}\).

(viii) The figure shows a triangle with sides labeled: \(2x + 4\), \(4x - 4\), and \(4x\).

Question 2

Construct AB || PQ such that the distance between AB and PQ is 12 cm.

Question 3

Draw AB = 11 cm. Take a point C outside AB. Construct CD || AB.

Question 4

The vertical angle in an isosceles triangle is \(3x - 5\) while a base angle is \(x\). Find the measure of all the angles of the triangle.

Question 5

An exterior angle of a triangle measures \(8x\) while one of its opposite interior angle measures \(\frac{5x}{7}\). If the other opposite interior angle measures \(66°\), find the value of \(x\).

Question 6

Identify the angles with the greatest and the least magnitudes in \(\triangle PQR\), given PQ = 3.56 cm, QR = 5.63 cm, and RP = 3.65 cm.

Question 7

Identify the longest and the shortest sides in \(\triangle ABC\) shown in Figure (i).

Figure (i) shows a triangle with angles marked as \(118°\) at vertex A and \(138°\) at vertex C.

Question 8

Construct \(\triangle ABC\), given AB = 6.5 cm, CA = 7.5 cm, and altitude AO = 6 cm.

Question 9

Construct \(\triangle ABC\) where AB = AC, given AB = 7.5 cm and \(\angle CAB = 60°\).

Question 10

(i) Construct equilateral \(\triangle PQR\), given its altitude PO = 6 cm.

(ii) Two triangles of a particular type are congruent to each other if their perimeters are equal. What type of triangles are they?

Question 11

If the base of an isosceles triangle measures 12 cm and its altitude from the vertex to the base measures 8 cm, find the measure of its equal sides.

Question 12

Find the measure of DE and \(\angle BCA\) in Figure (ii).

Figure (ii) shows a triangle with measurements: AD = 7 cm, AE = 5 cm, DE = 7 cm, DB = 11 cm, EC = 5 cm, and \(\angle ADE = 46°\).

Question 13

The vertical ladder of a 'slide' in a park is 7 feet high while the slide is 25 feet long. If a boy slides down from the top of the slide, how far from its base will he land?

Hint: see the sketch given in Figure (iii).

Figure (iii) shows a right triangle with sides labeled 25, 7, and hypotenuse.

Question 14

An angle in a quadrilateral measures \(135°\). If the other three angles are in the ratio \(3 : 5 : 7\), find all the angles of the quadrilateral.

Question 15

An angle in a quadrilateral measures \(96°\). If the other three angles are given as \(2x + 3\), \(3x + 4\), and \(4x + 5\), find all the angles of the quadrilateral.

Question 16

An exterior angle of a parallelogram measures \(107°\). Find all the angles of the parallelogram.

Question 17

The perimeter of a parallelogram with its sides in the ratio \(3 : 8\) is given to be 55 cm. Find the measure of two adjacent sides of the parallelogram.

Question 18

Construct quadrilateral ABCD, given AB = 7 cm, BC = 5 cm, CD = 8 cm, \(\angle ABC = 75°\), and \(\angle BCD = 90°\).

Question 19

Construct parallelogram EFGH, given EF = 9 cm, GH = 6 cm, and altitude GO = 4 cm.

Question 20

Construct rectangle IJKL, given diagonal JL = 9 cm and \(\angle IOK = 60°\) where diagonals IK and JL intersected at point O.

Question 21

Construct rhombus MNOP, given diagonal MO = 8.5 cm and \(\angle MNO = 60°\).

Question 22

Construct square QRST, given diagonal RT = 9 cm.

Question 23

Given AB = 9 cm and AD = 6 cm in rectangle ABCD shown in Figure (iv), find the area of \(\triangle ADE\).

Figure (iv) shows a rectangle ABCD with point E below the rectangle, where AB = 9 cm, ED = 6 cm, and ED = 5 cm.

Question 24

Find the sum of the interior angles of a polygon with 11 sides.

Question 25

How many diagonals can be drawn from the vertex in a polygon with 11 sides?

Question 26

Drawing diagonals from one vertex, how many triangles can be formed in a polygon with 11 sides?

Question 27

Find the measure of each interior angle of a regular polygon with 12 sides.

Question 28

How many sides are there in a regular polygon if each exterior angle measures \(18°\)?

Question 29

Is a regular polygon possible in which each exterior angle measures \(11.25°\)?

Question 30

(i) Construct the incircle of \(\triangle ABC\) given AB = AC, base BC = 6 cm, and altitude = 4 cm.

(ii) Construct the circumcircle of equilateral \(\triangle PQR\) given its height is 9 cm. Will the diameter of the circle be more than or less than 9 cm?

Question 31

What is the order of rotational symmetry of a ceiling fan with 3 blades, when seen from directly under the fan?

Question 32

Plot \(\triangle ABC\), given A(2, 2) B(9, 3) C(5, 8) and find its image \(A_1B_1C_1\) when reflected about the Y axis.

Question 33

Plot a pentagon A(0, 5) B(5, 0) C(11, 6) D(9, 10) E(3, 8) and find its image \(A_1B_1C_1D_1E_1\) when rotated anti-clockwise about the origin by \(90°\).

Question 34

When point A is rotated about the zero mark to point \(A_1\) on the number line, \(A_1\) represents the position of an irrational number on the number line. Apply the Pythagoras' theorem to find the irrational numbers represented by \(A_1\) in each of the following:

(i) A number line diagram showing a point A with coordinates approximately between 1 and 2.

(ii) A number line diagram showing a point A with coordinates approximately between 2 and 3.

(iii) A number line diagram showing a point A with coordinates approximately between 3 and 4.

This is a preview of the first 3 pages. To get the complete book, click below.