Construction of a Perpendicular Bisector

Q.

A line divides an angle in two equal parts is called a……….of angle.

1. (a) bisector

2. (b) exterior

3. (c) interior

Q.

Draw a perpendicular bisector of a line segment of a length $\overline{7.5cm}$

Q. To construct a perpendicular bisector, we need a ruler and a.

1. protractor
2. compass
3. set square

Q.

How many bisectors of a given angle can be drawn?

Q.

To bisect a line segment of length $7\mathrm{cm}$, the opening of compass should be more than ___________________.

Q. $\overline{MN}$ is the perpendicular bisector of the line segment $\overline{AB}$. If $\overline{AB}$ measures 6 cm, what is the length of $\overline{AN}$ and $\overline{NB}$?

Q.

It is possible to draw two bisectors of a given angle

1. True
2. False

Q. Draw a circle of radius 6 cm using ruler and compasses. Draw one of its diameters. Draw the perpendicular bisector of this diameter. Does this perpendicular bisector contain another diameter of the circle?

Q. Perpendicular bisector of a line segment divides the line segment into ____ equal parts.

1. four
2. three
3. two
4. six

Q. Arrange the following steps of construction of perpendicular lines in the correct order.
1. Draw a line using a ruler and mark a point.
2. Through the marked point draw a line along the edge.
3. Placing the ruler tightly and slide the set square along the ruler till the edge of the set square touches the marked point.
4. Place the ruler on the line and place one edge of a set square along the line.
5. Measure and check whether the obtained angle is ${90}^{\circ }.$

1. 1, 2, 3, 5, 4
2. 1, 4, 3, 2, 5
3. 3, 2, 4, 1, 5
4. 1, 4, 3, 5, 2

Q. On a circle of radius 3 cm draw its two chords. Then construct the perpendicular bisector of these chords. Where do they meet?

Q. A line segment has ____ perpendicular bisector(s)

1. two
2. four
3. one
4. three

Q. To constuct a perpendicular bisector of $\overline{AB}$ , the measure on the compass should be set _____ half of the length of AB.

1. more than
2. less than
3. None of the above
4. equal to

Q.

Ali was asked to construct a square for which, the diagonal alone is given(length unknown) and nothing else. He was given a compass and a straight edge (a ruler with NO markings). The square is ACBD. P is the point of intersection of the diagonals of the square. Which of the following is constructed as a first step in this construction?

1. B or CD, P, AP or PB or OC or OD

2. AC or CD, P, AP or PB or OC or OD

3. AB or BD, P, AP or PB or OC or OD

4. AD or CD, P, AP or PB or OC or OD

Q. If a perpendicular bisector bisects a line segment AB of 14 cm at C, then AC is ____ cm.

1. 6
2. 5
3. 8
4. 7

Q. Construct the following angles using set-squares:

(i) 45°
(ii) 90°
(iii) 60°
(iv) 105°
(v) 75°
(vi) 150°

Q. The length of AB is 16.If C is the midpoint of AB, then AC =

1. 16
2. 8
3. 4
4. 9

Q. Construct a tangent to a circle of radius $3cm$ from a point on the concentric circle of radius $5cm$ and measure its length. Also verify the measurement by actual calculation.

1. $5cm,verified$
2. $4cm,verified$
3. $5cm,ca{n}^{\prime }tbeverified$
4. $3cm,verified$

Q. Given a line BC and a point A on it, construct a ray AD using set squares so that ∠DAC is

(i) 30°
(ii)60°

Q. In $△$ CDE , $\angle$ C = 30° and $\overline{CD}$ = 8 cm. Which is the correct information needed to construct the triangle?

1. $△$ CDE is an isosceles triangle with base $\overline{DE}$
2. $△$ CDE is right angled at $\angle$E
3. $\overline{DE}$ = 11 cm and $\angle$ E = 80°
4. None of the above