Parallel Lines and Transversal

Q.

ABCD is a trapezium with $AB\parallel DC$. E and F are points on non-parallel sides AD and BC respectively such that $EF\parallel AB$. Then, $\frac{AE}{ED}=\frac{BF}{FC}$.

1. True

2. False

Q.

State true or false:

The parallel lines do intersect at infinity.

1. False

2. True

Q.

Two supplementary angles are in the ratio 2:3. What are their values(in degrees)?

1. 72 and 108

2. 30 and 150

3. 54 and 36

4. 45 and 135

Q.

Write the supplement of 180-x

Q.

In the given figure, AB || CD. Prove that p +q -r =180.

Q. In a triangle $ABC,AD$ is the median drawn on the side $BC$ is produced to $E$ such that $AD=ED$ prove that $ABEC$ is a parallelogram.

Q. Two lines are perpendicular to each other. Then the angle between the lines is

1. $0^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${90}^{\circ }$

Q.

Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.

Q.

In quadrilateral ABCD, diagonals AC and BD intersect at point E. Such that AE : EC = BE : ED. Then, ABCD is a parallelogram.

1. True

2. False

Q.

In the given figure, DE || BC, AE = 15cm, EC = 9cm, NC = 6 cm & BN = 24 cm. The value of ME & DM are

1. 3.75 & 15 cm respectively

2. 3 cm & 15.75 cm respectively

3. 3 cm & 15 cm respectively

4. 3.75 & 15.75 cm respectively

Q.

Two distinct lines :

1. Always intersect.

2. Either intersect or parallel.

3. Always have two common points.

4. Always parallel.

Q. An angle is 200 more than three times the given angle. If the two angles are supplementary the angles are?

Q.

Two distinct lines always intersect in a point. True or False?

1. False

2. True

Q.

From figure, identify the incorrect statement, given that l||m and t is transversal.

1. ∠2 and ∠8 are supplementary

2. ∠2 and ∠3 are supplementary

3. ∠2 and ∠5 are supplementary

4. ∠2 and ∠1 are supplementary

Q.

The angle between two lines is ${90}^{\circ },$ then the lines are ___ to each other.

1. parallel

2. transversal
3. adjacent
4. perpendicular

Q. Find the supplement of 112 degree 48 minute

Q. Find the measure of an angle which is 26 less than its supplementary.

Q.

In the figure given below, if BD = 2.4 cm, AC = 3.6 cm, PD = 4 cm, PB = 3.2 cm, and AC is parallel to BD, then the lengths of PA & PC will be

1. 4.8 cm and 6 cm respectively

2. 6.8 cm and 4 cm respectively

3. 6 cm and 4.8 cm respectively

4. 4 cm and 6.8 cm respectively

Q. One angle is equal to three times its supplement. The measure of the angle is

(a) 130°

(b) 135°

(c) 90°

(d) 120°

Q. The two edges of a straight road are examples for lines.

1. parallel
2. perpendicular
3. intersecting

Q. Prove that two lines perpendicular to same line are parallel to each other

Q.

The sides of a triangle are in the ratio $2:3:4$. If the perimeter is $27cm$, find the length of each side.

Q. Prove that the bisectors of two adjacent supplementary angles include a right angle.

Q.

Answer the following questions and justify.
(i) Can two acute angles he complement to each other?
(ii) Can two obtuse angles be complement to each other?
(iii) Can two right angles he complement to each other?
(iv) Can two acute angles be supplementary?
(v) Can two obtuse angles be supplementary?
(vi) Can two right angles be supplementary?
(vii) Can two adjacent angles be supplementary?
(viii) Can two adjacent angles be complementary?
(ix) Can two obtuse angles be adjacent angles?
(x) Can an acute angle be adjacent to an obtuse angle?
(xi) Can two acute angles form a linear pair?
(xii) can two obtuse angles form a linear pair?
(xiii) Can two right angles form a linear pair?

Q.

Find the measure of an angle which is equal to its supplement.

Q.

A line segment $AB$ is divided in the ratio $m:n$ where $m$ and $n$ are co-prime, using a single ray $AX$. The number of arcs to be drawn on $AX$ is _____.

1. m+n

2. m-n

3. m

4. n

Q.

In the above figure AB || CD. Also, ∠EAB = 84^o and ∠ECD = 126^o. Then, the value of "x" is

1. 80^o

2. 120^o

3. 150^o

4. 160^o

Q. Write the supplement of an angle of measure 2y°.

Q.

Find the Measure of an angle which is supplement of itself is :

1. 45^o

2. 30^o

3. 180^o

4. 90^o

Q. The supplement of an acute angle is .................