Question

In the figure 10.15, show that:
1) AB|| CD
(ii) CD || EF
(ii) AB || EF

Justify your answer.
​

Answer 1

$\huge\underline\bold\orange{Answer:}$

$\textbf{\underline{\underline{To\: show\:AB\:parallel\:to\:CD}}}$

When AB and CD are two lines and BC is transversal

$\implies\angle\:ABC = {40}^{\circ}$....equation 1

$\therefore\angle\:BCD = \angle\:BCE+ \angle\:ECD$

$\implies\angle\:BCD = {40}^{\circ}$....equation 2

From Equation 1 and 2 :

$\angle\:ABC = \angle\:BCD$

[Alternate Interior Angles]

$\therefore$ Alternate Interior Angles are equal then lines are parallel

Hence,

AB || CD (Proved]

$\textbf{\underline{\underline{To\: show\:CD\:parallel\:to\:EF}}}$

When CD and EF are two lines and EC is transversal.

From Construction- EF is produced at x

$\implies$CD || FX

At angle "E"

$\implies\angle\:FEC = \angle\:XEC = {180}^{\circ}$

$\implies{160}^{\circ} + \angle\:XEC = {180}^{\circ}$

$\implies\angle\:XEC = {20}^{\circ}$.....equation 1

Now,

$\angle\:ECD = {20}^{\circ}$ ....equation 2

From Equation 1 and 2 :

$\angle\:XEC = \angle\:ECD$

[Alternate Interior Angles]

$\therefore$ Alternate Interior Angles are equal then lines are parallel

Hence,

CD||EF (Proved)

$\textbf{\underline{\underline{To\: show\:AB\:parallel\:to\:EF}}}$

AB || CD...equation 1

CD || EF.....equation 2

From equation 1 and 2 :

AB || EF (Proved)

Answer 2

Answer:

1.To show that AB is Parallel to CD

Given $\angle$ABC = 40°

$\angle$BCD = 20° + 20° = 40°

So,

$\angle$ABC = $\angle$BCD (Alternate Interior)

So, AB is parallel to CD....{eq.1}

2. To show that CD is parallel to EF

$\angle$FEC + $\angle$ECD

160° + 20° = 180°

Sum of corresponding = 180°

Hence,CD is parallel to EF....{eq.2}

3.To show that AB is parallel to EF

When, AB is parallel to CD, CD is parallel to EF, Then, AB is parallel to EF

${\boxed{\tt{Hence\:Proved}}}$