Basic Constructions

Q.

Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisector rays are perpendicular to each other.

Q. Construct a angle of 110' ?

Q.

$\text{Construct each of the following angles, using ruler and compasses:}\left(i\right){75}^{\circ }\left(ii\right){37.5}^{\circ }\left(iii\right){135}^{\circ }\left(iv\right){22.5}^{\circ }$

Q.

Construct a segment of a circle given an angle of ${90}^{\circ }$ and chord 5 cm.

Q.

${70}^{\circ }$ can be constructed using a ruler and a compass.

1. False

2. True

Q.

Construct the following angles at the initial point of a given ray and justify the construction:

(i) ${45}^{\circ }$

(ii) ${90}^{\circ }$

Q.

Draw an obtuse angle. Bisect it. Measure each of the angles so obtained.

Q.

Construct the angles of the following measurements:

$\left(i\right){30}^0\left(ii\right){75}^0\left(iii\right){105}^0\left(iv\right){135}^0\left(v\right){15}^0\left(vi\right)22{\frac{1}{2}}^{\circ }$

Q.

Using your protractor, draw an angle of measure ${108}^{\circ }$. With this angle as given, draw an angle of ${54}^{\circ }$.

Q.

Using ruler and compasses only, draw an angle of measure ${135}^{\circ }$.

Q.

Draw an angle and label it as $\angle$BAC. Construct another angle, equal to $\angle$BAC.

Q.

Using a protractor, draw an angle of measure ${72}^{\circ }$. With this angle as given, draw angles of measure ${36}^{\circ }and{54}^{\circ }$.

Q.

A triangle ABC can be constructed in which $\angle$B = 105${}^{\circ }$, $\angle$C = 90${}^{\circ }$ and AB + BC + AC = 10 cm.

1. False

2. True

Q. Which of the following angles can be constructed with the help of just a ruler and a pair of compasses?

Q.

Which of the following instruments can be used to create a right angle?

1. Ruler

2. Compass

3. Set Square

4. Options 1 & 2

Q.

Using ruler and compasses only, draw a right angle.

Q. With the help of a ruler and a compass, it is possible to construct an angle of

1. 
   40°
2. 
   32.5°
3. 
   135°
4. 
   42.5°

Q. can be constructed with the help of just a ruler and a pair of compasses.

1. ${42.5}^{\circ }$
2. ${40}^{\circ }$
3. ${67.5}^{\circ }$
4. ${55}^{\circ }$

Q.

Explain, out of the three methods, using ruler, tracing and compasses, which method is the best and why?

Q.

Using compass construct the angle $105°$

Q. To construct a ${135}^{\circ }$ angle using a compass and ruler only, angles are required to be constructed.

1. 110° & 25°
2. 65°& 70°
3. 90°& 45°
4. 100°& 35°

Q. We use a compass to bisect an angle.

1. False
2. True

Q. Two tennis balls are the real life example of congruent shapes.

1. True
2. False

Q. When we bisect an angle of ${45}^{\circ }$ , we get two angles. ​​​​​

1. ${30}^{\circ }$
2. ${22.5}^{\circ }$
3. ${23.5}^{\circ }$
4. ${15}^{\circ }$

Q. Question 4 (ii)
Construct the following angles and verify by measuring them by a protractor:
(ii) ${105}^{\circ }$

Q. We cannot draw $\angle {180}^{\circ }$ without using a protactor or a compass.

1. False
2. True

Q.

What is the only possible angle(in degrees) that can be created by using a straight ruler alone?

Q.

Which of the following parameters given in the figure are enough to construct the figure (choose the minimum number of parameters possible):

Distance AO = d

Radius of the bigger circle (with center A) = R

Radius of the smaller circle (with center B) = r

$\angle$POA = $\theta$

Note that other than the parameters given in an option, nothing else is given and you have to come up with the figure as given above.

1. R, r, d, AO, BO

2. AO, BO, d

3. R, d, r

4. R, d,

Q. Question 1
Draw an angle of ${110}^{\circ }$ with the help of a protractor and bisect it. Measure each angle.

Q.

In a straight line, what is the first basic angle that would be obtained? (in degrees)

1. ${270}^{\circ }$
2. ${180}^{\circ }$
3. ${45}^{\circ }$
4. ${90}^{\circ }$