Understanding Quadrilaterals quiz

The sum of the interior angles of a pentagon is:

Each exterior angle of a regular hexagon measures:

A quadrilateral with exactly one pair of parallel sides is a:

The diagonals of a rhombus are always:

The number of diagonals of a hexagon is:

The opposite angles of a parallelogram are:

The sum of the exterior angles of an octagon is:

A regular polygon each of whose interior angles is 108 degrees is a:

A polygon in which at least one diagonal lies outside it is:

Two adjacent angles of a parallelogram are 2x and 3x. The value of x is:

Distinguish between a convex polygon and a concave polygon with one sketch of each. (2 marks)

Find the number of sides of a regular polygon each of whose exterior angles is 40 degrees. (2 marks)

Find the measure of each interior angle of a regular decagon. (2 marks)

In a parallelogram, one angle is three times its adjacent angle. Find all the angles. (2 marks)

State two properties of a kite. (2 marks)

Explain why a square is both a rectangle and a rhombus. (2 marks)

Can a quadrilateral have angles of 120, 90, 80 and 50 degrees? Give a reason. (2 marks)

The diagonal of a rectangle is 10 cm and one side is 6 cm. Find the other side. (2 marks)

Name two quadrilaterals whose diagonals are equal and bisect each other. (2 marks)

What is the smallest possible interior angle of a regular polygon? Explain why. (2 marks)

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find each angle and state what kind of quadrilateral it could be. (3 marks)

The angles of a pentagon are x, x + 10, x + 20, x + 30 and x + 40 degrees. Find x and each angle. (3 marks)

The sum of the interior angles of a polygon is 1440 degrees. Find the number of sides. If the polygon is regular, find each interior and each exterior angle. (3 marks)

The perimeter of a parallelogram is 150 cm. One of its sides is greater than the other by 25 cm. Find the lengths of all its sides. (3 marks)

In trapezium ABCD, AB is parallel to DC, angle A = 65 degrees and angle B = 70 degrees. Find angle D and angle C, giving reasons. (3 marks)

Read the passage and answer the questions. Honeybees build their combs from regular hexagonal cells, and many floors are also tiled with regular hexagons that fit together without gaps. (i) Find each interior angle of a regular hexagon. (ii) Explain why exactly three hexagons meet at each corner of the tiling. (iii) Can regular pentagons be used to tile a floor without gaps? Give a reason. (5 marks)

Read the passage and answer the questions. Kabir made a paper kite ABCD with AB = AD and CB = CD. The angle at A is 100 degrees and the angle at C is 60 degrees. The diagonal AC is the line of symmetry of the kite. (i) Find angles B and D. (ii) Find angle BAC, giving a reason. (iii) At what angle do the diagonals AC and BD meet? (5 marks)

Read the passage and answer the questions. A folding gate is made of metal strips that form identical parallelograms. In one position, an angle of each parallelogram is 50 degrees. Each parallelogram has sides 30 cm and 20 cm. (i) Find the other three angles of each parallelogram. (ii) Find the perimeter of one parallelogram. (iii) What shape does each parallelogram become when the angle becomes 90 degrees? (5 marks)

Read the passage and answer the questions. A STOP sign on the road is in the shape of a regular octagon. (i) Find the sum of its interior angles. (ii) Find the measure of each interior angle. (iii) Find each exterior angle and verify that the exterior angles add up to 360 degrees. (5 marks)

Read the passage and answer the questions. A garden plot ABCD is a parallelogram whose diagonals AC = 24 m and BD = 18 m cross each other at right angles at O. (i) What special type of parallelogram is the plot? Give a reason. (ii) Find the length of each side. (iii) Find the length of fencing needed and the area of the plot. (5 marks)

Draw a quadrilateral, a pentagon and a hexagon, and divide each into triangles by drawing diagonals from one vertex. Use the diagrams to derive the formula (n - 2) x 180 degrees for the angle sum of a polygon, and find the angle sum of a polygon with 12 sides. (6 marks)

Draw parallelogram ABCD with its diagonals meeting at O. State four properties of a parallelogram. Using the diagonal AC and congruent triangles, explain why the opposite sides of a parallelogram are equal. (6 marks)

Draw a rhombus, a rectangle and a square, each with its diagonals. State the properties of the diagonals of each figure. A rhombus has side 6 cm and one angle of 60 degrees; find the length of its shorter diagonal, giving a reason. (6 marks)

Draw a pentagon and show one exterior angle at each vertex. Explain, by imagining walking around the polygon, why the exterior angles add up to 360 degrees. Find the number of sides of regular polygons with exterior angles of 72 degrees and 30 degrees, and each interior angle of a regular polygon with 20 sides. (6 marks)

Draw a Venn diagram classifying quadrilaterals, showing trapeziums, kites, parallelograms, rectangles, rhombuses and squares. Use it to name the quadrilaterals in which (i) the diagonals bisect each other (ii) the diagonals are perpendicular (iii) the diagonals are equal. (6 marks)