**Exercise 17.1**

*Q1. Draw an \(\angle BAC\) of measure \(50^{\circ}\) such that AB = 5cm and AC=7 cm. Through C draw a line parallel to AB and through B draw a line parallel to AC, intersecting each other at D. Measure BD and CD*

__Steps of construction: __

Draw angle BAC = \(50^{\circ}\)

Cut an arc through C at an angle of \(50^{\circ}\)

Draw a straight line passing through C and the arc. This line will be parallel to AB since \(\angle CAB\)

Alternate angles are equal; therefore the line is parallel to AB.

Again through B, cut an arc at an angle of \(50^{\circ}\)

\(\angle SBA\)

Also we can measure BD = 7 cm and CD = 5 cm.

*Q2 Draw a line PQ.Â Draw another line parallel to PQ at a distance of 3 cm from it. *

__Steps of construction:__

- Draw a line PQ.
- Take any two points A and B on the line.
- Construct \(\angle PBF\)
=\(90^{\circ}\) and \(\angle QAE\) =\(90^{\circ}\) - With A as centre and radius 3 cm cut AE at C.
- With B as centre and radius 3 cm cut BF at D.
- Join CD and produce it on either side to get the required line parallel to AB and at a distance of 5 cm from it.

*Q3 Take any three non-collinear points A, B, C and draw \(\angle ABC\). Through each vertex of the triangle, draw a line parallel to the opposite side.*

__Steps of construction:__

- Mark three non collinear points A, B and C such that none of them lie on the same line.
- Join AB, BC and CA to form triangle ABC.

**Parallel line to AC **

- With A as centre, draw an arc cutting AC and AB at T and U, respectively.
- With centre B and the same radius as in the previous step, draw an arc on the opposite side of AB to cut AB at X.
- With centre X and radius equal to TU, draw an arc cutting the arc drawn in the previous step at Y.
- Join BY and produce in both directions to obtain the line parallel to AC.

__Parallel line to AB __

- With B as centre, draw an arc cutting BC and BA at W and V, respectively.
- With centre C and the same radius as in the previous step, draw an arc on the opposite side of BC to cut BC at P.
- With centre P and radius equal to WV, draw an arc cutting the arc drawn in the previous step at Q.
- Join CQ and produce in both directions to obtain the line parallel to AB.

__Parallel line to BC __

- With B as centre, draw an arc cutting BC and BA at W and V, respectively (already drawn).
- With centre A and the same radius as in the previous step, draw an arc on the opposite side of AB to cut AB at R.
- With centre R and radius equal to WV, draw an arc cutting the arc drawn in the previous step at S.
- Join AS and produce in both directions to obtain the line parallel to BC.

*Q4. Draw two parallel lines at a distance of 5kms apart.*

__Steps of construction:__

- Draw a line PQ.
- Take any two points A and B on the line.
- Construct \(\angle PBF\)
=\(90^{\circ}\) and \(\angle QAE\) =\(90^{\circ}\) < - With A as centre and radius 5 cm cut AE at C.
- With B as centre and radius 5 cm cut BF at D.
- Join CD and produce it on either side to get the required line parallel to AB and at a distance of 5 cm from it.