Practical Geometry quiz

The instrument used to draw a circle is a:

The instrument used to measure an angle is a:

The perpendicular bisector of a line segment makes an angle of:

Bisecting an angle of 60 degrees gives two angles of:

To construct an angle of 45 degrees, we bisect an angle of:

How many perpendiculars can be drawn to a line through a point on it?

Which angle cannot be constructed using only a ruler and compass?

A pair of set squares has angles of:

The bisector of a 180 degree angle makes angles of:

Points on the perpendicular bisector of AB are:

Write the steps to draw a circle of radius 3.2 cm. (2 marks)

How do you copy a line segment AB using a compass without measuring it? (2 marks)

Name the instruments needed to construct an angle of 60 degrees. (2 marks)

What is the measure of each angle when an angle of 150 degrees is bisected? (2 marks)

Draw a line segment of 6.8 cm and mark its midpoint by construction. Write the steps briefly. (2 marks)

How can you check whether a constructed angle bisector is correct? (2 marks)

Explain how an angle of 120 degrees is obtained using arcs of the same radius. (2 marks)

Draw any angle and copy it using a compass, without using a protractor. Write two steps. (2 marks)

Which special angles can be made by putting the two set squares together? Name any two. (2 marks)

Why should we not erase the construction arcs? (2 marks)

AB = 5.6 cm and CD = 3.9 cm. Find the length of a segment equal to AB + CD and of a segment equal to 2AB - CD. (3 marks)

An angle of 90 degrees is bisected and one of the parts is bisected again. Find the measure of each angle at each stage. What angle is obtained if 90 degrees and the 45 degrees part are added? (3 marks)

The perpendicular bisector of PQ meets it at O. If PO = 4.7 cm, find PQ. If a point S on the bisector is 6 cm from P, how far is it from Q? (3 marks)

Find the measure of the angle obtained when (i) 60 degrees and 30 degrees are constructed adjacent to each other (ii) 120 degrees and 30 degrees adjacent (iii) half of 135 degrees. (3 marks)

A circle has a diameter of 11 cm. Find the radius to which the compass should be set. If four equal radii are drawn at right angles, find the angle between neighbouring radii. (3 marks)

Read the passage and answer the questions. Meera wants to plant a tree exactly midway between two poles P and Q that are 12 m apart, and also at equal distance from both. She draws a scale diagram where 1 cm represents 1 m. (i) What length should she draw for PQ on the diagram? (ii) Which construction will help her find points equidistant from P and Q? (iii) How far from each pole is the midpoint in real life? (5 marks)

Read the passage and answer the questions. A carpenter needs to cut a wooden board at exactly 45 degrees for a picture frame corner but does not have a protractor. He has a compass and a straight edge. (i) Which angle should he construct first? (ii) What should he do next to get 45 degrees? (iii) If two such 45 degree pieces are joined, what angle is formed at the corner? (5 marks)

Read the passage and answer the questions. In an art class, students were asked to draw a six-petal flower. They drew a circle of radius 4 cm and, keeping the same radius, cut arcs one after another along the circle starting from a point on it. (i) How many arcs do they need to go around the circle once? (ii) What angle at the centre does each arc correspond to? (iii) Which special angle construction does this method use? (5 marks)

Read the passage and answer the questions. A road AB runs straight. A school S is located away from the road. The town planner wants to build the shortest path from the school to the road. (i) Which construction gives the shortest path from S to the road? (ii) What angle will the path make with the road? (iii) Write the first step of this construction. (5 marks)

Read the passage and answer the questions. Tanu drew an angle of 80 degrees with a protractor. She bisected it using a compass and then bisected one of the halves again. (i) What is the measure of each half? (ii) What is the measure after the second bisection? (iii) What is the total of the three smaller angles if one 40 degree part and two 20 degree parts are taken? (5 marks)

Draw a line segment PQ = 7.8 cm. Construct its perpendicular bisector. Mark the midpoint M and a point R on the bisector. Measure RP and RQ. Write the steps and state the property of points on the perpendicular bisector. (6 marks)

Construct an angle of 60 degrees with ruler and compass. Then bisect it to get 30 degrees and bisect again to get 15 degrees. Write the steps of each construction. (6 marks)

Construct an angle of 90 degrees at a point on a line using ruler and compass. Bisect it to obtain 45 degrees. Then construct 135 degrees on the same line. Write the steps. (6 marks)

Draw any angle ABC. Copy it at a new point P to form angle QPR without using a protractor. Then construct the bisector of angle QPR. Write the steps and explain why the copy is exact. (6 marks)

Draw a circle with centre O and radius 4 cm. Draw a chord AB of length 6 cm. Construct the perpendicular bisector of AB and show that it passes through O. Draw another chord and repeat. Explain how this helps to locate the centre of a circle. (6 marks)