Condition for 2 Lines to Be Parallel

Q.

If two non parallel lines lie in the same plane, the lines are ___.

1. perpendicular

2. Intersecting

3. concurrent

4. parallel

Q.

A transversal is a line that intersects two lines that are always parallel.

1. False

2. True

Q.

Parallel lines never intersect each other.

1. True

2. False

Q.

Ravi drew two lines L and M on a sheet of paper and a third line N to intersect these two lines. He observed that the angles formed by the intersection of the lines L and N were equal to the corresponding angles formed between M and N. What can be said about the lines?

1. Lines L and M are parallel

2. Lines L, M and N are parallel to each other

3. Line N is perpendicular to both the lines L and M

4. Lines L and M are perpendicular

Q.

"Only one transversal can be drawn for given two lines". True/False?

1. True

2. False

Q. In Fig., AB and CD are parallel lines intersected by a transversal PQ at L and M respectively. If ∠CMQ = 60°, find all other angles in the figure.

Q.

Refer the image below:

The horizontal lines will be parallel if

1. $\angle$ 1 = $\angle$ 4

2. $\angle$ 2 = $\angle$5

3. $\angle$ 4 = $\angle$ 6

4. $\angle$ 1 = $\angle$ 5

Q. In the figure, AB is parallel to CD, if ∠1 + ∠3 = 240°, then find the value of ∠6.

1. 125°
2. 60°
3. 75°
4. 90°

Q. In Fig., AB and CD are parallel lines intersected by a transversal PQ at L and M respectively. If ∠LMD = 35° find ∠ALM and ∠PLA.

Q.

When two lines are intersected by a transversal, what are conditions for these lines to be parallel?

1. When alternate interior angles are equal.

2. When interior angles on the same side of transversal are equal.

3. When corresponding angles are equal.

4. When interior angles on the same side of transversal are supplementary.

Q.

Question 49

Fill in the blanks to make the statement true.

Two lines in a plane which do not meet at a point anywhere, are called ___ lines.

Q. In Fig., AB || CD and a transversal PQ cuts them at L and M respectively. If ∠QMD = 100°, find all other angles.

Q. Line $l_1$ is parallel to $l_2$ and line $l_2$ is parallel to $l_3$, then line $l_1$ is parallel to $l_3$

1. False
2. True

Q. The line which intersects two distinct parallel lines in a plane at two distinct points is called a transversal.

1. True
2. False

Q.

In Fig., line $l\parallel m$ and a transversal $n$ cuts them at $P$ and $Q$ respectively. If $\angle 1={75}^{\circ }$, find all other angles.

Q. Line $l_1$ is parallel to $l_2$ and line $l_2$ is parallel to $l_3$, then line $l_1$ is parallel to $l_3$

1. False
2. True

Q. A perpendicular line passing through two parallel lines is a transversal.

1. True
2. False

Q. If two lines and a transversal form corresponding angles that are equal, then the lines are parallel.

1. False
2. True

Q. In Fig., AB || CD and ∠1 and ∠2 are in the ratio 3 : 2. Determine all angles from 1 to 8.

Q. Ravi drew two lines L and M on a sheet of paper and a third line N to intersect these two lines. He observed that the angles formed by the intersection of the lines L and N were equal to the corresponding angles formed between M and N. What can be said about the lines?

1. Lines L and M are perpendicular
2. Lines L and M are parallel
3. Line N is perpendicular to both the lines L and M
4. Lines L, M and N are parallel to each other

Q. In Fig., a transversal n cuts two lines l and m such that ∠2 = 65° and ∠8 = 65°. Are the lines parallel?

Q. In the given figure, l || m and t is a transversal.
If ∠5 = 70°, find the measure of each of the angles
∠1, ∠3, ∠4 and ∠8.

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. Shubh is right but Aju is wrong

3. Both Aju and Shubh are right

4. Aju is right but Shubh is wrong

Q.

In the figure given below, l and m are two parallel lines. Which of the following statement is true?

1. $\angle$1 + $\angle$8 = 180${}^{\circ }$
2. $\angle$7 + $\angle$8 + $\angle$5= 180${}^{\circ }$
3. $\angle$1 + $\angle$2 + $\angle$4 = 180${}^{\circ }$
4. $\angle$3 + $\angle$5 + $\angle$6 = 180${}^{\circ }$

Q. Ravi drew two lines L and M on a sheet of paper and a third line N to intersect these two lines. He observed that the angles formed by the intersection of the lines L and N were equal to the corresponding angles formed between M and N. What can be said about the lines?

1. Lines L and M are perpendicular
2. Lines L and M are parallel
3. Line N is perpendicular to both the lines L and M
4. Lines L, M and N are parallel to each other

Q.

In the following figure, m is parallel to \(\overset{\longleftrightarrow}{PB}\) , \(\angle 1\) = \(55^\circ\). True/False

Q. In Fig., if AB || CD and CD || EF, find ∠ACE.

Q. In Fig., line l || m and n is a transversal. If ∠1 = 40°, find all the angles and check that all corresponding angles and alternate angles are equal.

Q. In Fig., line l || m. Find the values of a, b, c, d. Give reasons.