Understanding Quadrilaterals | Chapter Assessment | English | Grade 8

Which of the following is false with respect to a rectangle?

• All angles are right angles

• Opposite sides are equal and parallel

• Diagonals are equal

• Diagonals are perpendicular to each other

Answer explanation

Diagonals of a rectangle do not intersect at each other at right angles. Hence they are not perpendicular to each other.

Identify the polygon from the given figures which is not a trapezium.

• 
• 
• 
• 

Answer explanation

The figure shown in option 1, 2 and 3 are all trapezium because all of them have four sides and one pair of opposite sides is parallel. The figure shown in option 4 is not a quadrilateral and hence it could not be a trapezium. it has five sides hence it is a pentagon.

For finding diagonals through vertex C of a Hexagon ABCDEF, C must be joined to _________.

• A, B, and D

• A, E and F

• D, E and F

• A and F only

Answer explanation

A diagonal of a polygon is a line segment that connects two nonconsecutive vertices. For getting diagonals through vertex C of a Hexagon ABCDEF, C ,must be joined to A, E and F because A, E and F are nonconsecutive vertices of vertex C.

What is the maximum measure of an exterior angle possible for a regular polygon?

• 60°

• 120°

• 180°

• 360°

Answer explanation

The exterior angle of a regular polygon = 360°/n where n is the number of sides of the regular polygon. To have maximum value of exterior angle the value of n must be minimum. But the smallest possible value of n is 3 Hence, the maximum measure of exterior angle of a regular polygon = 360°/3 = 120° which is the measure of each exterior angle of an equilateral triangle. Hence, option 2 is the correct answer.

Identify the odd one out.

• 
• 
• 
• 

Answer explanation

The polygons shown in option 2, 3 and 4 are all hexagon but the polygon shown in option 1 is a quadrilateral. Hence, the polygon shown in option 1 does not fit in the group.

A regular polygon has 8 sides. What will be the sum of interior angles of the polygon?

• 800°

• 720°

• 360°

• 1080°

Answer explanation

The eight sided polygon is an octagon. The sum of interior angles of a regular polygon = (n-2) x 180° where n is the number of sides of the polygon. here, since n = 8 Sum of interior angles of octagon = (8-2) x 180° = 6 x 180° = 1080° hence option 4 is correct

What is the length of a diagonal of the rectangle ABCD, if AO = 6x - 7 and DO = 4x + 5 and all lengths are measured in cm?

• 58 cm

• 29 cm

• 6 cm

• Can not be determined

Answer explanation

It is given that quadrilateral ABCD is a rectangle. In every rectangle the length of diagonals is equal Hence, AC = BD-----(1) Also diagonals in rectangle bisects each other. Hence 1/2 AC = 1/2 BD i.e. AO = DO i.e. 6x - 7 = 4x + 5 i.e. 6x - 4x = 5 + 7 i.e. 2x = 12 i.e. x = 12/2 i.e. x = 6 Since x = 6, AO = (6 x 6) - 7 = 36 - 7 = 29 cm Since AO = 29 cm therefore, AC = 2AO = 2 x 29 cm = 58 cm From (1), BD = 58cm

What is the value of diagonal MK in the given kite JKLM?

• 8 cm

• 6 cm

• 21 cm

• 25 cm

Answer explanation

In kite JKLM, Since the diagonals of a kite are perpendicular to each other, Hence, MK is perpendicular to JL therefore In ∆MIL, ∠MIL = 90° Applying pythagoras theorem ML² = MI² + IL² i.e. 17² = 15² + IL² i.e. IL² = 17² - 15² = 289 - 225 = 64 Therefore IL = 8 cm In kite JKLM, the longer diagonal MK divides the shorter diagonal JL into two equal parts. Hence, JI = IL = 8 cm In ∆JIK, ∠JIK = 90° Applying pythagoras theorem JK² = JI² + IK² i.e. 10² = 8² + IK² i.e. IK² = 10² - 8² = 100 - 64 = 36 Therefore IK = 6 cm So, the length of diagonal MK = MI + IK = 15 cm + 6 cm = 21 cm

If ABCD is a square, what is the value of x - y?

• 45°

• 40°

• 80°

• 90°

Answer explanation

Since, ABCD is a square, the diagonals must be intersecting each other at right angle. So, ∠COB = ∠COD = ∠DOA = ∠AOB = x = 90° In △AOB, ∠AOB = 90° ∠OAB = 45° Using angle sum property ∠AOB + ∠OAB + ∠ABO = 180° So, ∠ABO = 180° - (∠AOB + ∠OAB) i.e. ∠ABO = 180° - (90° + 45°) i.e. ∠ABO = 180° - 135° i.e. ∠ABO = 45° = y So, x - y = 90° - 45° = 45°