Constructions of a Line Parallel to a Given Line at a Given Distance from It.

Q. In following figure (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).

Q.

Draw a line MN = 5.8 cm. Locate a point A which is 4.5 cm from M and 5 cm from N. Through A draw a line parallel to line MN.

Q.

Draw a straight line AB = 6.5 cm. Draw another line which is parallel to AB at a distance of 2.8 cm from it.

Q.

Construct an angle PQR = ${80}^{\circ }$. Draw a line parallel to PQ at a distance of 3 cm from it and another line parallel to QR at a distance of 3.5 cm from it. Mark the point of intersection of these parallel lines as A.

Q.

Draw the perpendicular bisector of a line segment of length 7 cm and also find and mark the midpoint. [2 MARKS]

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. b, a, c

3. b, c, a

4. c, a, b

Q.

Find the ratio in which D divides side BC if $\frac{Ar\left(\Delta ABD\right)}{Ar\left(\Delta ADC\right)}=\frac{2}{3}$

1. $\frac{4}{3}$

2. $\sqrt{\frac{2}{3}}$

3. $1$

4. $\frac{2}{3}$

Q.

Mention the proper order of identifying a point D on BC such that $\frac{Ar\left(△ABD\right)}{Ar\left(△ADC\right)}=\frac{2}{3}$.
1) Join $B_{5}C$ and draw a line parallel to $B_{5}C$ from $B_2$.
2) Identify the ratio in which the point D divides BC using the relation given.
3) Mark 5 points B₁, B₂, B₃, B₄ and B₅ on BX such that they are equidistant.
4) Construct a ray BX which makes an acute angle with line segment BC.
5) The point of intersection of the parallel line from B₂ with BC is the point D.

1. 2, 4, 3, 1, 5

2. 1, 2, 4, 3, 5

3. 4, 3, 2, 5, 1

4. 3, 5, 2, 4, 1

Q.

Find the ratio in which D divides side BC if $\frac{Ar\left(\Delta ABD\right)}{Ar\left(\Delta ADC\right)}=\frac{2}{3}$.

1. $\sqrt{\frac{2}{3}}$

2. $\frac{2}{3}$

3. $1$

4. $\frac{4}{3}$

Q. Divide line segment AB measuring 7 cm in the ratio 3 : 2.

Q.

Given a base angle B and the difference of the sides AC and AB (not necessarily in this order), what is the difference in the steps of constructions when

i) AC $>$ AB

ii) AC $<$ AB

1. Instead of drawing the perpendicular bisector of line segment BC, we’ll draw the angle bisector of angle B in this case

2. Instead of plotting the point D on the ray BX as (AC – AB) = say 2units, we rewrite it as (AB – AC) = -2 units and plot the point D 2 units down south of point B on the same ray BX.

3. Instead of having B as the base angle, have the same construction with C as the base angle

4. None of the above

Q. Draw a line MN=5.8cm. Locate point A which is 4.5cm from M and 5cm from N. Through A draw a line parallel to line MN.

Q. Construct a cyclic quadrilateral $PQRS$ in which $PQ$ $=5$ cm, $QR$ $=6$ cm, $PR$ $=3.5$ cm and $RS$ $=5$ cm.

Q.

Mention the proper order of identifying a point D on BC such that $\frac{Ar\left(△ABD\right)}{Ar\left(△ADC\right)}=\frac{2}{3}$?
1) Join $B_{5}C$ and draw a line parallel to $B_{5}C$ from $B_2$.
2) Identify the ratio in which the point D divides BC using the relation given.
3) Mark 5 points B₁, B₂, B₃, B₄ and B₅ on BX such that they are equidistant.
4) Construct a ray BX which makes an acute angle with line segment BC.
5) The point of intersection of the parallel line from B₂ with BC is the point D.

1. 1, 2, 4, 3, 5

2. 4, 3, 2, 1, 5

3. 3, 5, 2, 4, 1

4. 2, 4, 3, 1, 5