# RD Sharma Solutions Class 7 Constructions Exercise 17.1

### 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:

Step 1: Draw angle BAC = $(50^{\circ})$ Where AC = 7 cm and AB = 5 cm.

Step 2: Cut an arc through C at an angle of $(50^{\circ})$

Draw a straight line passing through C and the arc.

We know that, Alternate angles are equal. The line passing through C is parallel to AB.

Which implies, $(\angle CAB) = (\angle RCA)= (50^{\circ})$

Step 3: Cut an arc at an angle of $(50^{\circ}$ at point B and draw a line passing through B. Here we can see that this line is parallel to AC.

Therefore BD parallel to AC and alternate angles are equal.

Step 4: Measure the length of BD and CD

BD = 7 cm and CD = 5 cm.

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

Steps of construction:

Step 1: Draw a line PQ.

Step 2: Choose two twos points on the line, say A and B.

Step 3: Construct right angles at points A and B

$(\angle PBF)= (90^{\circ})$and$(\angle QAE)=(90^{\circ})$

Step 4: Choose A as centre and radius 3 cm cut AE at C.

With B as centre and radius 3 cm cut BF at D.

Step 5: Join CD with the help of a ruler and produce it on either side to get the required line parallel to AB and at a distance of 5 cm.

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:

1. Draw 3 non-collinear points, say, A, B and C such that none of them lies on the same line.

2. Form a triangle ABC by joining AB, BC and CA.

3. Construct a Parallel line to AB

• Choose B as a centre, draw an arc cutting BC and BA at W and V, respectively.
• Choose C as a centre and draw an arc on the opposite side of BC to cut BC at P. (Note: use the same radius as in the previous step)
• 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.

4. Construct a Parallel line to AC

• With A as centre, draw an arc cutting AC and AB at T and U, respectively.
• With centre B and draw an arc on the opposite side of AB to cut AB at X. (Note: use the same radius as in the previous step)
• 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.

5. Construct a Parallel line to BC

• With B as a centre, draw an arc cutting BC and BA at W and V, respectively (already drawn).
• With centre A and draw an arc on the opposite side of AB to cut AB at R. (Note: use the same radius as in the previous step)
• 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.

3. construct $(\angle PBF)= (90^{\circ})$and$(\angle QAE)=(90^{\circ})$