RD Sharma Solutions Class 7 Constructions Exercise 17.1

RD Sharma Class 7 Solutions Chapter 17 Ex 17.1 PDF Free Download

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

RD Sharma Solutions Class 7 Constructions

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.

Class 7 Constructions

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.

Class 7 Examples on Constructions

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.

6. Your construction is ready.

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

Parallel Lines Construction

Steps of construction:

  1. Draw a line PQ.
  2. Choose any two points on the line, say A and B.
  3. construct \((\angle PBF)= (90^{\circ})\)and\((\angle QAE)=(90^{\circ})\)
  4. Set radius as 5 cm and cut AE at C, where A is the centre point.
  5. Cut BF at D, With B as centre and radius 5 cm.
  6. 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.
  7. Your construction is ready.

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