Properties of Angles Formed by Two Parallel Lines and a Transversal

Q. Question 1
In figure, if $\angle BAC={90}^{\circ }andAD\perp BC$. Then,


(A) $BD.CD=B{C}^2$
(B) $AB.AC=B{C}^2$
(C) $BD.CD=A{D}^2$
(D) $AB.AC=A{D}^2$

Q. In $△ABC$ and $△PQR,\angle A={30}^o,\angle B={70}^o,\angle P={70}^o,\angle Q={80}^o$ and $AB=RP,$ then

1. $△ABC\cong △PQR$
2. $△ABC\cong △QRP$
3. $△ABC\cong △RPQ$
4. $△ABC\cong △PRQ$

Q.

In the given figure, $POQ$ is a line, then the value of $x$ is

1. 
2. 
3. 
4. 

Q.

Two lines in the same plane that do not intersect are called _______ lines.

Q.

Prove that the right bisector of a chord of a circle, bisects the corresponding arc of the circle.

Q. If two parallel lines are cut by a transversal, then:

1. each pair of alternate angles are equal

2. each pair of alternate angles add up to ${180}^o$
3. each pair of corresponding angles add up to ${180}^o$.

4. each pair of corresponding angles is equal.

Q. In the adjoining figure, if line m II line n and line p is a transversal then find x.

1. ${90}^o$
2. ${50}^o$
3. ${45}^o$
4. ${135}^o$

Q. Each pair of interior angles formed by two parallel lines and their transversal is _______.

1. equal
2. supplementary
3. complementary
4. ${90}^{\circ }$ each

Q.

Find out the complements of the angle :

81$°$

Q.

Prove that the line joining the midpoints of two parallel chords of a circle passes through the centre.

Q.

What are intersecting lines and parallel lines?

Q.

Question 14 (iii)
In the adjoining figure, name the following pairs of angles:
Equal supplementary angles.

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. In triangle PQR, PQ = PR and PM is perpendicular to QR. By which property is triangle PQM congruent to triangle PRM?

1. SSS
2. SAS
3. AAS
4. RHS

Q.

In the figure given below, angle A and angle B are

1. adjacent angles

2. vertically opposite angles

3. supplementary angles

4. corresponding angles

Q.

Fill in the blanks:

Two lines in a plane that do not meet at a point anywhere are called ________.

Q.

Classify the following True or False:

The supplement of an acute angle is always an obtuse angle.

1. True
2. False

Q.

Statement $1$: When two lines intersect each other, only the angles forming linear pair are supplementary.

Statement $2$: When two lines intersect each other, angles forming linear pair are supplementary.

Choose the correct option.

1. Both the statements are correct.

2. Statement $1$ is correct but statement $2$ is incorrect.

3. Statement $2$ is correct but statement $1$ is incorrect.

4. Both the statements are incorrect.

Q.

Find the value of angles 2, 3, 4 if the value of angle 1 is 45. [4 MARKS]

Q.

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

1. Corresponding angles

2. Alternate angles

3. Vertically opposite angles

4. Interior opposite angles (co-interior angles)

Q.

Each pair of interior angles formed by two parallel lines and their traversals are ............... angles. ?

Q.

In the given figure AB || CD. If $\angle EGD={140}^{\circ }$ and $\angle GHB=4x^{\circ }$, then find the value of x.

1. ${30}^{\circ }$

2. ${35}^{\circ }$

3. ${40}^{\circ }$

4. ${45}^{\circ }$

Q. In the adjoining figure, line p II line l II line q. Find $\angle x$ with the help of the measures given in the figure.

1. ${50}^o$
2. ${60}^o$
3. ${65}^o$
4. ${70}^o$

Q.

Question 14 (ii)
In the adjoining figure, name the following pairs of angles:
Adjacent complementary angles.

Q.

Find the supplement angle of $\frac{1}{4}$ right angle .

Q.

Find the supplement angle of $57°$.

Q.

_________ are the lines that are always the same distance apart and never intersect.

Q. If in $△ABC\text{and}△PQR$, AB = PQ, $\angle A=\angle P\text{and}\angle B=\angle Q$, then by what rule is $△ABC\text{congruent to}△PQR?$

1. RHS
2. AAS
3. SSS
4. SAS

Q.

Question 12 (i)
Find the values of the angles x, y and z in each of the following:

Q.

Question 80

In the given figure OR $\perp$ OP,

(i) Name all the pairs of adjacent angles.
(ii) Name all the pairs fo complementary angles.