Basic Constructions

Q.

Which of the following angles cannot be constructed with a ruler and compass ?

1. ${80}^{\circ }$

2. ${90}^{\circ }$

3. ${60}^{\circ }$

4. ${105}^{\circ }$

Q.

Construct an angle of ${45}^{\circ }$ without using protractor by the method of angle bisection. Any of the other geometric instruments can be used.
[3 MARKS]

Q. Construct an angle of ${105}^{\circ }$ using a compass and verify by measuring it by a protractor [2 MARKS]

Q.

Construct an angle bisector for an angle of ${70}^{\circ }$ using a compass. [2 MARKS]

Q.

What is the use of geometric construction?

Q.

Construct a trapezium ABCD in which AB = 6 cm, BC = 4 cm, CD = 3.2 cm, $\angle B={75}^{\circ }$ and DC || AB.

Q.

It is possible to construct an angle of 52.5${}^{\circ }$ with the help of compass and ruler.

1. True

2. False

Q.

Draw a trapezium ABCD in which AB || DC, AB = 7 cm, BC = 5 cm, AD = 6.5 cm and $\angle B={60}^{\circ }$

Q.

Pavan tried to draw a line parallel to a given line, 'l'. Few steps are shown below. What will be the next step?

Step 1: Mark a point A, not on the line 'l'.
Step 2: Mark point B on line 'l'.
Step 3: Draw line segment joining points A and B.
Step 4: Draw an arc with B as the centre, such that it intersects line 'l' at D and AB at E.

1. Draw another arc with the same radius and A as the centre, such that it intersects AB at F

2. Draw another arc with B as the centre and distance DE as the radius

3. Draw another arc with some other radius and A as the centre

4. Draw another arc with B as the centre and distance DE as the radius

Q.

Follow the following steps of constructions:
(a) Draw a line l and mention a point O on it.
(b) With O as center and a short radius, draw an arc that cuts line l at A.
(c) With A as center and the same radius (as in step 2), draw an arc that cuts the first arc at B.
(d) Join O and B. Extend OB to get a ray.
What is the measure of ∠AOB (in degrees)?

1. 45

2. 60

3. 90

4. 75

Q.

In the given figure if $\angle$ BAC = ${60}^{\circ }$, then which of the following statements are true?

1. AB=AC

2. AB=BC

3. BC = AC

4. none of the above

Q.

Which among the following angles cannot be constructed just by using a ruler and a compass?

1. 30 degrees

2. 60 degrees

3. 70 degrees

4. 90 degrees

Q.

Which of the following angles can be constructed without using a protractor?

1. 30${}^{\circ }$

2. 40${}^{\circ }$

3. 50${}^{\circ }$
4. 60${}^{\circ }$

Q.

How many degrees are there in half of a right angle.

Q. Select the method/methods used for constructing a perpendicular to a line from a point outside the line.

1. by folding a paper
2. using a set square
3. using a compass and ruler
4. all the above

Q.

For drawing a geometric construction, 2 instruments are enough.

1. True

2. False

Q.

Look at the figure below:

To draw a line parallel to l through A, the first step will be:

1. Join A to B

2. Join A to l

3. Draw perpendicular from A on l

4. Draw a line through A.

Q. With the help of a ruler and , we can draw geometrical figures of given lengths and angles.

1. compass
2. divider
3. set square

Q.

It is possible to construct an angle of 135° with the help of compass and ruler.

1. True

2. False

Q.

Which of the following instruments are not used in constructions?

1. Compass

2. Set Squares

3. Protractor

4. None of These

Q.

Draw a line segment with length 7 cm. Now, draw arcs at one end with radius 3 cm and another end with radius 4 cm. The two arcs drawn will intersect at a point.

1. True

2. False

Q.

For which of the following applications is precise geometric constructions not necessary?

1. Design of tools

2. World maps

3. None of These

4. Building construction

Q. With the help of a ruler and a compass it is not possible to construct an angle of

1. ${37.5}^{\circ }$
2. ${40}^{\circ }$
3. ${22.5}^{\circ }$
4. ${67.5}^{\circ }$

Q. Construct a trapezium $RISK$ in which $RI\parallel KS$, $RI=7cm,IS=5cm,RK=6.5cm$ and $\angle I={60}^{\circ }$.

Q. Construct a trapezium $RISK$ in which $RI\parallel KS$, $RI=7cm,IS=5cm,RK=6.5cm$ and $\angle I={60}^{\circ }$.

Q.

With a ruler and compass which of the following angles cannot be constructed?

1. ${80}^{\circ }$

2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${105}^{\circ }$

Q.

With a ruler and compass which of the following angles cannot be constructed?

1. ${160}^{\circ }$

2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${105}^{\circ }$

Q.

See the figure below:

To draw a line parallel to l through A, the next step will be

1. Draw a line parallel to l through A

2. Cut the arc GF equal to the arc CD

3. Draw a line through A

4. Draw an angle of 60^o at G.

Q.

Draw a line AB. Take a point P outside it. Draw a line passing through P and parallel to AB.

Q.

Which instrument would you use to draw an arc?

1. Ruler

2. Compass

3. Divider

4. Protracter