Quadrilaterals quiz

The sum of the angles of a quadrilateral is:

The diagonals of a parallelogram:

A quadrilateral with all sides equal and all angles 90 degrees is a:

The diagonals of a rhombus are:

In a parallelogram, opposite angles are:

The line segment joining the mid-points of two sides of a triangle is:

If one angle of a parallelogram is 70 degrees, the adjacent angle is:

Which quadrilateral has exactly one pair of parallel sides?

The diagonals of a rectangle are:

In triangle PQR, the mid-points of PQ and PR are joined. If QR = 9 cm, the length of the joining segment is:

Three angles of a quadrilateral are 75, 90 and 75 degrees. Find the fourth angle. (2 marks)

Show that each angle of a rectangle is 90 degrees, using the property of a parallelogram. (2 marks)

Can all the angles of a quadrilateral be acute? Give a reason. (2 marks)

In a parallelogram, one side is 8 cm and the perimeter is 30 cm. Find the other sides. (2 marks)

Why is every square a rhombus but not every rhombus a square? (2 marks)

The diagonals of a parallelogram ABCD meet at O. If AO = 5 cm and BO = 7 cm, find AC and BD. (2 marks)

Prove that a quadrilateral with each pair of opposite angles equal is a parallelogram. (2 marks)

In a rhombus, one diagonal is equal to a side. Find the angles of the rhombus. (2 marks)

State the converse of the Mid-point Theorem. (2 marks)

Show that the bisectors of two adjacent angles of a parallelogram meet at a right angle. (2 marks)

The angles of a quadrilateral are x, 2x, 3x and 4x degrees. Find the angles. (3 marks)

The perimeter of a rhombus is 52 cm and one diagonal is 24 cm. Find the other diagonal. (3 marks)

In a triangle, the sides are 8 cm, 10 cm and 12 cm. Find the perimeter of the triangle formed by joining the mid-points of its sides. (3 marks)

In parallelogram PQRS, angle P is 30 degrees less than twice angle Q. Find all angles. (3 marks)

A rectangle has a diagonal of 25 cm and one side of 7 cm. Find the other side, its area and the length of the other diagonal. (3 marks)

Read the passage and answer the questions. A kite frame is made of two sticks crossing each other at right angles. The sticks are 60 cm and 80 cm long and bisect each other, forming a rhombus-shaped kite. (i) Find the side of the kite. (ii) Find its perimeter. (iii) Name the property of the rhombus used. (5 marks)

Read the passage and answer the questions. A rectangular playground ABCD has diagonals AC and BD crossing at O. The length is 40 m and the breadth is 30 m. (i) Find the length of each diagonal. (ii) Find OA. (iii) What property of rectangles does this show? (5 marks)

Read the passage and answer the questions. A triangular park PQR has sides PQ = 30 m, QR = 40 m and PR = 50 m. A path joins the mid-points M of PQ and N of PR. (i) Find the length of MN. (ii) Is MN parallel to QR? Give a reason. (iii) Find the perimeter of triangle PMN. (5 marks)

Read the passage and answer the questions. A carpenter checks whether a wooden frame is a parallelogram by measuring its diagonals. He finds that they bisect each other. (i) Is the frame a parallelogram? Why? (ii) If the diagonals are also equal, what shape is it? (iii) If they are equal and perpendicular, what shape is it? (5 marks)

Read the passage and answer the questions. A tiled floor has tiles in the shape of a parallelogram with one angle 60 degrees and sides 10 cm and 6 cm. (i) Find the other angles. (ii) Find the perimeter of a tile. (iii) Are the diagonals of a tile equal? Explain. (5 marks)

Prove the Mid-point Theorem with a neat figure. Use it to show that the four triangles formed by joining the mid-points of the sides of a triangle are congruent. (6 marks)

Prove that a diagonal divides a parallelogram into two congruent triangles. Hence prove that the opposite sides and opposite angles of a parallelogram are equal. (6 marks)

Prove that a quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel. Draw a figure. (6 marks)

Show that the diagonals of a rhombus are perpendicular to each other. Find the area of a rhombus with diagonals 10 cm and 24 cm, and its side. (6 marks)

ABCD is a trapezium with AB parallel to DC. E is the mid-point of AD, and a line through E parallel to AB meets BC at F. Prove that F is the mid-point of BC. Draw a neat figure. (6 marks)