Practical Geometry quiz

The number of independent measurements needed to construct a unique quadrilateral is:

The minimum number of measurements needed to construct a square is:

The diagonals of a rhombus bisect each other at an angle of:

The sum of the angles of a quadrilateral is:

In quadrilateral ABCD, angle A = 80 degrees, angle B = 95 degrees and angle C = 105 degrees. Angle D is:

The instrument used to draw arcs of a given radius is:

A quadrilateral with all sides 4 cm and all angles 90 degrees is a:

To construct a quadrilateral given four sides and one diagonal, we first construct:

The diagonals of a rhombus are 6 cm and 8 cm. Its side is:

A triangle with sides 3 cm, 4 cm and 8 cm:

Why does a quadrilateral need five measurements for its construction, whereas a triangle needs only three? (2 marks)

List the four sets of given measurements for which you have learnt to construct a general quadrilateral. (2 marks)

Explain why knowing the length of one side is enough to construct a square. (2 marks)

How many measurements are needed to construct a rectangle? Name them and give a reason. (2 marks)

Three angles of a quadrilateral are 70 degrees, 110 degrees and 95 degrees. Find the fourth angle. (2 marks)

How can the property "the diagonals of a rectangle are equal and bisect each other" be used to construct a rectangle when a diagonal and a side are known? (2 marks)

One angle of a parallelogram is 65 degrees. Find its other three angles. (2 marks)

Can a quadrilateral ABCD be constructed with AB = 5 cm, BC = 6 cm and AC = 12 cm? Give a reason. (2 marks)

Why should a rough sketch be drawn before constructing a quadrilateral? (2 marks)

State two properties of a kite that help in its construction. (2 marks)

The diagonals of a rhombus are 10 cm and 24 cm. Find its side, perimeter and area. (3 marks)

A diagonal of a rectangle is 13 cm and one side is 5 cm. Find the other side, the perimeter and the area. (3 marks)

The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. Find all four angles. Can such a quadrilateral be constructed? (3 marks)

(i) Find the area and the diagonal (to two decimal places) of a square of side 6 cm. (ii) Find the area of a square whose diagonal is 8 cm. (3 marks)

The adjacent sides of a parallelogram are 5 cm and 7 cm and one angle is 70 degrees. Find its other angles and its perimeter. (3 marks)

Read the passage and answer the questions. A surveyor measures a field ABCD and finds AB = 30 m, BC = 40 m, CD = 30 m, DA = 40 m and the diagonal AC = 50 m. She wants to draw the field on paper using the scale 1 cm = 10 m. (i) Write the lengths she will draw on paper. (ii) Show that triangle ABC has a right angle at B. (iii) What type of quadrilateral is the field? Find its area. (5 marks)

Read the passage and answer the questions. To make a kite, Arjun ties two thin sticks of lengths 40 cm and 60 cm at right angles. The shorter stick is tied across the longer one at a point 20 cm from its top, and the shorter stick is bisected by the longer one. (i) Find the lengths of the two upper sides and the two lower sides of the kite to one decimal place. (ii) Find the area of paper needed to cover the kite. (iii) Using the scale 1 cm = 10 cm, describe how Arjun can construct an accurate drawing of the kite. (5 marks)

Read the passage and answer the questions. A floor is to be covered with identical tiles shaped like a rhombus. Each tile has diagonals of 4 cm and 3 cm. (i) Find the side of each tile. (ii) Find the area of each tile. (iii) Write the steps for constructing an accurate drawing of one tile. (5 marks)

Read the passage and answer the questions. Asha tried to construct quadrilateral ABCD with AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm, but she could not complete the construction. (i) Explain why her construction failed. (ii) Between which limits must AC lie so that both triangles ABC and ACD can be drawn? (iii) Suggest a value of AC for which the construction is possible, and state which triangle she should draw first. (5 marks)

Read the passage and answer the questions. A town planner wants to draw a plot ABCD in which the two roads AC and BD crossing the plot are 6 km and 5 km long, and the boundaries AB = 3 km, BC = 4 km and AD = 3.5 km. (i) Which case of quadrilateral construction is this? (ii) Which triangle should be drawn first, and why? (iii) Write the steps to complete the construction. (5 marks)

Construct quadrilateral JUMP with JU = 3.5 cm, UM = 4 cm, MP = 5 cm, PJ = 4.5 cm and PU = 6.5 cm. Draw a rough sketch first, write the steps of construction and show all arcs. (6 marks)

Construct quadrilateral LIFT with LI = 4 cm, IF = 3 cm, TL = 2.5 cm, LF = 4.5 cm and IT = 4 cm. Draw a rough sketch, write the steps, and explain why this is the case of two diagonals and three sides. (6 marks)

Construct quadrilateral MORE with MO = 6 cm, OR = 4.5 cm, angle M = 60 degrees, angle O = 105 degrees and angle R = 105 degrees. Write the steps of construction, then calculate angle E and check it by measurement. (6 marks)

Construct quadrilateral PLAN with PL = 4 cm, LA = 6.5 cm, angle P = 90 degrees, angle A = 110 degrees and angle N = 85 degrees. First find angle L, then draw a rough sketch and write the steps of construction. (6 marks)

Construct a rhombus BEST with BE = 4.5 cm and diagonal ET = 6 cm. Write the steps of construction, measure the other diagonal BS, and check your measurement by calculation using the properties of a rhombus. (6 marks)