Perpendicular Lines

Q.

Two distinct lines meeting at a point are called ______ lines.

1. Intersecting

2. Parallel

3. Segment

4. All of above

Q.

How many angles are formed when two lines intersect?

1. One

2. Two

3. Three

4. Four

Q. Give some real-life examples of parallel lines.

Q. Write the different names of the line.

Q.

The angle between two perpendicular line is ___

1. $90$ degree

2. $90$

3. ${90}^{\circ }$

4. $90$ degrees

Q. What cross-sections do you get when you give a vertical cut to a cylindrical rod (Refer figure)?

1. Circle
2. Triangle
3. Rectangle
4. None of these

Q.

Which of the following is an example of perpendicular lines?

1. Corners of your circular room floor.

2. One of the angles in both the set squares of geometry box.

3. Angle included between the hour hand and minute hand when it is $12:15$ in your wall clock.

1. 1
2. 2
3. 2 and 3
4. 1 and 3

Q. Two lines perpendicular to another line are each other .

1. perpendicular to
2. parallel to
3. intersecting

Q.

Steps for constructing a line segment whose length is equal to the difference of the lengths of the two given line segments are:

(i) Now draw a line L.

(ii) Take two line segments AB and CD.

(iii) With P as a centre cut a length PZ equal to AB.

(iv) SZ is the required line Segment.

(v) Mark point P on the line L.

(vi) Now from P cut a length PS equal to CD.

1. vi, iv, ii, i, v, iii

2. ii, i, v, iii, vi, iv

3. v, iii, vi, iv, ii, i

4. ii, i, vi, iv, v, iii

Q.

NO and PQ are

1. Intersecting lines

2. Rays

3. Parallel lines

4. Line segments

Q.

Two lines which cut each other at a point are called ………. lines

Q.

Intersecting lines have ________ point/s in common.

1. zero

2. one

3. two

4. three

Q. Parallel lines are two non - intersecting lines. State whether the statement is true or false.

1. True
2. False

Q. Steps for the construction of perpendicular bisector PQ to a line segment AB of given length is given below. Choose the correct order.
1.With B as the centre and the same radius as in previous step, draw two arcs to intersect the arcs drawn in previous step. Name the point of intersection of the arcs as P and Q
2.Draw a line segment AB of given length using a scale.
3.Join P and Q.
4.With A as the centre and radius more than half of AB, draw two arcs (using compases) above & below AB

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

Q. Line XY is __________ to line AB.

1. parallel
2. perpendicular
3. equal
4. less than

Q.

Write correct sequence of the following steps to draw perpendicular bisector of a line AB.

a. Join XY to cut AB at O. XY is called the perpendicular bisector of AB.

b. To construct the perpendicular bisector of the line segment AB, we first take A and then B as centre and radius greater than half of AB.

c. Draw arcs above and below AB such that the arcs cut each other at X and Y.

1. a, b, c

2. c, a, b

3. b, c, a

4. b, a, c

Q.

AB is a line of length 6 cm. Construct a line perpendicular to AB. [4 MARKS]

Q.

If OD is perpendicular to AB, and ∠DOC = 25°, find ∠BOC - ∠AOC.

1. 25°

2. 115°

3. 65°

4. 50°

Q.

All closed figures are polygons.

1. True
2. False

Q. Which of the following represent perpendicular lines?

1. 
   The line segments from the letter V
2. 
   Adjacent edges of a carrom board
3. 
   The rails of a railway track
4. 
   Steps of a ladder

Q.

You start from your home at point A and run 100 m in West direction to reach point B. After that, you run 50 m in East direction to reach point C. Then you run 100 m in a South direction and reach point D. Which of the following is true?

1. $AB\perp BC$

2. $AB\perp CB$

3. $AD\perp CB$

4. $BC\perp CD$

Q. AD, BE and CF are three concurrent lines in a triangle ABC meeting the opposite sides in D, E and F respectively. Show that the joins of the midpoints of BC, CA and AB to the midpoints of AD, BE and CF are concurrent.

Q. Steps for the construction of a perpendicular to AB from an outside point P is given below. Choose the correct order.
1.With radius more than half of XY draw an arc above AB , X as centre
2.Using a scale, join PQ. Mark the intersection point of PQ and AB as ‘O’. Now PQ is perpendicular to AB
3.With a suitable radius and P as the centre draw an arc which cuts AB at X and Y
4.Draw a straight line AB and mark a point P lying outside AB
5.With Y as centre draw another arc, with same radius chosen in previous step, that cuts the previous arc. Name the point of intersection as Q

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

Q.

Which are parallel segments or lines?

1. 

2. 

3. 

Q. Three points A, B, C are on the same straight line. If AB = 5cm 6 mm and AC = 10cm 2mm. Then BC = ?

1. 2cm 4mm
2. 12cm 5mm
3. 6cm 4mm
4. 4cm 6mm

Q. We can directly draw a perpendicular to a line at a point on the line using a protractor without using a compass.

1. False
2. True

Q. Perpendicular lines can be drawn using a ______ and a ruler.

1. divider
2. compass
3. pencil
4. none of the above

Q. In this figure, the line XY is _____ to AB.

1. perpendicular
2. parallel
3. plane
4. ray

Q.

You start from your home at A and run for 100m in west direction to reach point B. After that, you run for 50m in east direction to reach point C. Then you run for 100m in a South direction and reach point D. Which of the following is true?

1. AB ⊥ ​BC

2. BC ⊥ CD

3. AB ⊥ CB

4. AD ⊥ CB

Q. A perpendicular is drawn to a line segment $\overline{MN}$ at N using a protractor and a point P is marked on it. Which of the following is true?

1. $\overline{MP}$ $\perp$ $\overline{NP}$
2. $\overline{MN}$ $\perp$ $\overline{MP}$
3. $\overline{MN}$ = $\overline{MP}$
4. $\overline{MN}$ $\perp$ $\overline{NP}$