Tag: constructing a perpendicular bisector

Questions Related to constructing a perpendicular bisector

If $PQ$ is the perpendicular bisector of $AB$, then $PQ$ divides $AB$ in the ratio:

maths geometrical construction constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. $1:2$

  2. $1:3$

  3. $2:3$

  4. $1:1$

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Correct Option: D
Explanation:

Perpendicular bisector always divides a segment into two equal parts.
Therefore $PQ$ divides $AB$ into $1:1$.

For drawing the perpendicular bisector of $PQ$, which of the following radii can be taken to draw arcs from $P$ and $Q$?

maths geometrical construction constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

  1. $\dfrac{PQ}2$

  2. $\dfrac{PQ}3$

  3. $\dfrac{2PQ}3$

  4. $\dfrac{PQ}4$

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Correct Option: C
Explanation:

To draw a perpendicular bisector of a given side, take any length that is greater than half the length of the side. Draw the arcs from the edges of the base. The point where arcs meet is on the perpendicular bisector.


From the given options,

$\dfrac{2PQ}{3}$ can be considered to draw to draw arcs from edges $P, \ Q$

Remaining options has the value $\leq \dfrac{PQ}{2}$

The instrument in the geometry box having the shape of a triangle is called a 

maths plane geometry line and angle set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. Protractor

  2. Compasses

  3. Divider

  4. Set-square

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Correct Option: D
Explanation:

The instrument in the geometry box having the shape of a triangle are called set-squares

Two parallel lines have _____ slopes.

maths plane geometry line and angle set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. opposite

  2. equal

  3. negative

  4. different

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Correct Option: B
Explanation:

Two parallel lines have equal slopes as they are at the same inclination with the positive direction of X-axis. Also, the coefficients of $x$ and $y$ of two parallel lines are in proportion.

Option $B$ is correct.

In the sides a,b,c of a triangle ABC are in A.P then $\dfrac{b}{c}$ belong to

maths plane geometry line and angle set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. $(0, \dfrac{2}{3})$

  2. $(1,2)$

  3. $(\dfrac{2}{3}, 2)$

  4. $(\dfrac{2}{3}, \dfrac{7}{3})$

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Correct Option: A

With compasses and ruler, construct with each of the following angles:

maths when lines join set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. 60 $ ^{\circ} $

  2. 30 $ ^{\circ} $

  3. 90 $ ^{\circ} $

  4. 45 $ ^{\circ} $

  5. 22 $\frac{1}{2} ^{\circ} $

  6. 75 $ ^{\circ} $

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Correct Option: A
State True or False:
An angle of $52.5$ can be constructed using the compass.
maths when lines join set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. True

  2. False

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Correct Option: A
Explanation:

 As $52.5 =\frac{210^{\circ}}{4} \ and \   210 =180 + 30 $  and we can bisect the angle, so given angle can be constructed.

So True.