Parallel Lines

Transversal: When a line cuts or intercepts the parallel lines, then that line is called as transversal line.

Intercept: When a line meets or cuts another line then that intersection point is known as intercept point.

By observing the above figure we can say that there are three parallel lines (g,h,l) and one transversal (q)

There are three intercepts (D, E, F).

This figure is similar to the above figure, but we have one more transversal line here.

∴ we have 2 transversal lines (p, s) because they are not parallel to each other.

In this figure we can take any set(t,v) or (s, p, k) of parallel lines because they are perpendicular to each other.

However, I am assuming t, v as transversal lines.

Given figure consists of 3 parallel lines (lines k, l, m) and 2 transversals (lines c, d)

So, 5-line segments are formed. They are, XY, YZ, PQ, QR, XP, YQ, and ZR

Length of segment XY l(XY) = 5cm

Length of segment YZ l(YZ) = 3cm

Length of segment PQ l(PQ) = 5.5cm

We have to find l(QR)

According to the property of 3 parallel lines and their transversal

∴

l(PQ) = 3.3

∴ length of segment l(PQ) is 3.3cm

From the figure we can say that the lines a, b, c parallel to each other and they are equidistance to each other.

So, length of segment PQ and length of segment QR

∴ l(PQ) = l(QR)

∴ l(PQ) =7.2 cm

Similarly, l(LM) = l(MN)

6.2 = l(MN)

∴ l(MN) = 6.2 cm.

i. Firstly, we have to draw a line segment LM of length 9 cm

ii. Draw a line with an acute angle from point L. Point the compass on L, and cut the new line with some radius (here I can’t make an arc so that I pointed it as A)

iii. Place the compass along the line and make 5 arcs. Since we need 5 congruent parts, and name the last one as M’

iv. Take length of MO as radius draw an arc from L just below it. Again, take the length of LO as radius and draw an arc which cuts the previous arc from M, name the intersection point as L’

v. Connect L’ and M,

vi. Taking the same length that we used in line LM’, draw arcs along L’M. Connect the points along LM’ and L’M

vii. Name the intercepts on the LM line as J,K,N,O and observe all segments are divided equally.

i. Firstly we have to draw a line segment CD of length 6.4 cm

ii. Draw a line with an acute angle from point C

iii. Point the compass on C, and cut the new line with some radius

iv. Place the compass along the line and make 3 arcs. Since we need 3 congruent parts, and name the last one as “F”

v. Take length of DF as radius draw an arc from C just below it. Again, take the length of CF as radius and draw an arc which cuts the previous arc from D, name the intersection point as D’

vi. Connect D and D’

vii. Taking the same length that we used in line CC’, draw arcs along DD’.

viii. Connect the points along CC’ and DD’ and name the intercepts along CD as I, J

And observe the equal length segments.

i. In this we are asked to divide it in 2:3 ratio

So, 2+3 = 5

5, number congruent of line segment is formed.

ii. In this we are asked to divide it in 1:5 ratio

So, 1+5 = 6

6, number congruent of line segment is formed.

iii. In this we are asked to divide it in 1:2 ratio

So, 1+2 = 3

3, number congruent of line segment is formed.

iv In this we are asked to divide it in 3:4 ratio

So, 3+4 = 7

7, number congruent of line segment is formed.

V. In this we are asked to divide it in 5:3 ratio

So, 5+3 = 8

8, number congruent of line segment is formed.

In this we are asked to divide it in 2:3 ratio

So, 2+3 = 5

5, number congruent of line segment is formed.

i. Firstly, we have to draw a line segment ST of length 10 cm

ii. Draw a line with an acute angle from point s

iii. Point the compass on S, and cut the new line with some radius

iv. lace the compass along the line and make 5 arcs. Since we need 5 congruent parts, and name the last one as “E”

v. Take length of TE as radius draw an arc from S just below it.

Again, take the length of SE as radius and draw an arc which cuts the previous arc from T, name the intersection point as F. Connect F and T

vi. Taking the same length that we used in line SE, draw arcs along FT

vii. Connect the points along SE and FT and name the intercepts on line ST as K,L,M,N

viii. Thus we can divide a line segment as SL:LT = 4:6

= 2:3

In this we are asked to divide it in 2:3 ratio

So, 3+2 = 5

5, number congruent of line segment is formed.

i. Firstly, we have to draw a line segment AB of length 7 cm. Draw a line with an acute angle from point A

ii. Point the compass on A, and cut the new line with some radius

place the compass along the line and make 5 arcs. Since we need 5 congruent parts, and name the last one as “G”

iii. Take length of BG as radius draw an arc from A just below it.

Again, take the length of AG as radius and draw an arc which cuts the previous arc from B, name the intersection point as H

Connect B and H

iv. Taking the same length that we used in line AG, draw arcs along BH and name the points.

v. Connect the points along AG and BH. Name the intercepts on the line AB as M, N, O & P.

vi. Thus we can divide a line segment as AO:OB = 6:4

= 3:2

In this we are asked to divide it in 1:2 ratio

So, 1+2 = 3

3, number congruent of line segment is formed.

i. Firstly, we have to draw a line segment PQ of length 6 cm

Draw a line with an acute angle from point P

ii. Point the compass on P, and cut the new line with some radius

iii. Place the compass along the line and make 3 arcs. Since we need 3 congruent parts, and name the last one as “F”

iv. Take length of QF as radius draw an arc from P just below it. Again, take the length of PF as radius and draw an arc which cuts the previous arc from Q, name the intersection point as Q’. Connect Q and F

v. Taking the same length that we used in line PP’, draw arcs along QQ’

vi. Connect the points along PP’ and QQ’. Name the intercepts on the line PQ as J, K

vii. Thus we divided a line segment as PJ:JQ = 2:4

= 1:2

In this we are asked to divide it in 4:1 ratio

So, 4+1 = 5

i. Firstly, we have to draw a line segment PQ of length 7 cm

Draw a line with an acute angle from point P

ii. Point the compass on P, and cut the new line with some radius

iii. Place the compass along the line and make 5 arcs. Since we need 5 congruent parts, and name the last one as “E”

iv. Take length of EQ as radius draw an arc from P just below it.

v. Again, take the length of PE as radius and draw an arc which cuts the previous arc from Q, name the intersection point as G. Connect Q and G

vi. Taking the same length that we used in line PP’, draw arcs along GQ and name the points as H, I, J, K

vii. Connect the points along QS and PT

viii. Thus we have divided the line segment as PR:RQ = 4:1