Question

Draw a line segment AB of 4 cm in length. Draw a line perpendicular to AB through A and B, respectively. Are these lines parallel?​

Answer 1

${\huge\fbox\pink{A}\fbox\blue{n}\fbox\purple{S}\fbox\green{w}\fbox\red{E}\fbox\orange{r}}$

• To draw a line perpendicular to AB through A and B, respectively.

Use the following steps of construction.

• Draw a line segment AB = 4 cm.

• Taking 4 as centre and radius more than ½ AB (i.e., 2 cm) draw an arc say it intersect AB at E.

• Taking E as centre and with same radius as above draw an arc which intersect previous arc at F.

• Again, taking F as centre and with same radius as above draw an arc which intersect previous arc (obtained in step II) at G.

• Taking G and F are centres, draw arcs which intersect each other at H.

• Join AH . Thus, AX is perpendicular to AB at A. similarly, draw BY ⊥ AB at B.

Now,

we know that if two lines are parallel, then the angle between them will be 0° or 180°.

Here,

∠XAB = 90° [∴ XA ⊥ AB] and ∠YBA = 90°

[ ∴ YB ⊥ AB] ∠XAB + ∠YBA = 90° + 90° = 180° So, the lines XA and YS are parallel.

[since, it sum of interior angle on same side of transversal is 180°, then the two lines are parallel]

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$\sf\red{Thank\:you!}$

Answer 2

Answer:

Always happy

srry for not responding