## Chapter 10 Practical Geometry Exercise 10.1

**Question 1: Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.Answer:**

Actual Figure

Steps for construction

1. Draw a line AB.

2. Take any point Q on AB and a point P outside AB and join PQ.

3. With Q as centre and any radius draw an arc to cut AB at E and PQ at F.

4. With P as centre and same radius draw an arc IJ to cut QP at G.

5. Place the pointed tip of the compass at E and adjust the opening so that the pencil tip is at F.

6. With the same opening as in step 5 and with G as centre, draw an arc cutting the arc IJ at H.

7. Join PH to draw a line CD.**Question 2: Draw a line L. Draw a perpendicular to L at any point on L. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to L.Answer:**

Actual Figure

Steps for construction

1. Draw a line L.

2. Take any point P on line L.

3. At point P, draw a perpendicular line N.

4. Place the pointed tip of the compass at P and adjust the compass up to length of 4 cm, draw an arc to cut this perpendicular at point X.

5. At point X, again draw a perpendicular line M.

**Question 3: Let L be a line and P be a point not on L. Through P, draw a line m parallel to L. Now join P to any point Q on L. Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet L at S. What shape do the two sets of parallel lines enclose?**

Answer:

Answer:

Actual Figure

Steps for construction

1. Draw a line L.

2. Take any point Q on L and a point P outside L and join PQ.

3. Make sure that angles at point P and point Q are equal i.e. ∠Q = ∠P

4. At point P extend line to get line M which is parallel L.

5. Then take any point R on line M.

6. At point R draw angle such that ∠P = ∠R

7. At point R extend line which intersects line L at S and draw a line RS.

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