Parallel Lines with a Transversal

Q. angles formed when a transversal intersects two parallel lines are supplementary

1. Corresponding
2. Alternate
3. Co-interior
4. Congruent

Q.

Question 35

State whether the given statement is True or False.

If line PQ || line m, then line segment PQ || m.

Q. Match the following with respect to a transversal that intersects two parallel lines.

1. are equal
2. supplementary
3. 2 distinct point
4. do not meet

Q. If line segment PQ || line m, and line m || line n, then what is the relation between PQ and line n ?

1. $PQ\parallel linen$
2. $PQ\perp linen$
3. $PQ=linen$
4. $\text{None of these}$

Q. What are corresponding, vertically, alternate, co-interior angles?

Q.

Draw a line segment AB. Mark a point L approximately 3 cm above AB. Through L draw $\mathrm{LM}\parallel \mathrm{AB}$.

Q. A/An intersects two lines at two distinct points.

1. circle
2. angle
3. transversal

Q. Mark four points A, B, C and D in your notebook such that no three of them are collinear. Draw all the lines which join them in pairs as shown in Fig. 10.23.


(i) How many such lines can be drawn?
(ii) Write the names of these lines.
(iii) Name the lines which are concurrent at A.

Q.

Given two parallel lines and a transversal, which of the following pair of angles are equal?

1. Co-interior angles

2. Alternate interior angles

3. Adjacent angles

4. Alternate exterior angles

Q.

Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as centre an arc FG is drawn (as shown in the figure).

What is the relation between $\angle$FAG and $\angle$MBD?

1. alternate exterior angles
2. alternate interior angles
3. corresponding angles
4. vertically opposite angles

Q.

Which of the following pair of angles formed are not equal (always) when a transversal intersects two parallel lines?

1. Vertically opposite angles

2. Corresponding angles

3. Alternate angles

4. Co-interior angles

Q. Which of the following can't be the measure (in degrees) of an internal angle in any polygon?

1. 90
2. 108
3. 200
4. 180

Q. Match column A and column B with the help of the Fig. 15. 18:

Column A		Column B
i	Vertically opposite angles	a	∠PAB and ∠ABS
ii	Alternate angles	b	∠PAB and ∠RBY
iii	Corresponding angles	c	∠PAB and ∠XAQ

Q. angles formed when a transversal intersects two parallel lines are supplementary

1. Corresponding
2. Alternate
3. Co-interior
4. Congruent

Q.

When a transversal intersects two parallel lines, the corresponding angles so formed will be

1. supplementary
2. complementary
3. equal

Q.

Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as centre an arc FG is drawn (as shown in the figure).

What is the relation between $\angle$FAG and $\angle$MBD?

1. alternate exterior angles
2. alternate interior angles
3. corresponding angles
4. vertically opposite angles

Q.

Given two parallel lines and a transversal, which of the following pair of angles are not equal?

1. Co-interior angles

2. Alternate interior angles

3. Adjacent angles

4. Alternate exterior angles

Q. Match the following with respect to a transversal that intersects two parallel lines.

1. are equal
2. supplementary
3. 2 distinct point
4. do not meet

Q. In the figure alongside, four points P, Q, R and S are given, Draw lines, each passing through any two of the points. Then answer these questions.


(1) Name the lines whose points of concurrence is Q.
(2) Which of the lines PS, SR, QS and PR are concurrent?

Q.

Given line 'm' is parallel to line 'l'. Find x?

1. 45°

2. 65°

3. 35°

4. 85°

Q.

If $\angle 1+\angle 2=180,$then $l$and $m$are ___________.

Q.

<Two friends arguing>

Aju: A transversal is a line which intersects two lines at two distinct points.

Shubh: A transversal is a line which intersects two parallel lines at two distinct points.

1. Both Aju and Shubh are wrong

2. Both Aju and Shubh are right

3. Aju is right but Shubh is wrong

4. Shubh is right but Aju is wrong

Q.

Navi said that railway lines are parallel, whereas Shashank said that railway lines are not parallel. Who is correct and why?
[2 MARKS]

Q.

Can a circle has pair of parallel diameters $?$

Q.

Are line a and b shown in the adjacent figure parallel? Give a reason.

Q.

Which of the following pair of angles formed are not equal when a transversal intersects two parallel lines?

1. Corresponding angles

2. Vertically opposite angles

3. Alternate angles

4. Co-interior angles

Q.

Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as centre an arc FG is drawn (as shown in the figure).

What is the relation between length of arc DM and arc FG?

1. Length (Arc FG) = 2 x Length (Arc DM)

2. Length (Arc FG) = (1/2) x Length (Arc DM)

3. Length (Arc FG) = (3/2) x Length (Arc DM)

4. Length (Arc FG) = Length (Arc DM)

Q.

Given two parallel lines and a transversal, which of the following pair of angles are equal?

1. Co-interior angles

2. Alternate interior angles

3. Adjacent angles

4. Alternate exterior angles