**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.

Solution:

Steps of construction:

(i) Draw a line AB.

(ii) Take any point D on it.

(iii) Join the given point C to D and mark ∠1 to ∠CDB.

(iv) Mark ∠1 = ∠2 at C and produce to both side.

(v) MN is the required line.

Using the Property of Alternate Angles

Question 2.

Draw a line Z. 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.

Solution: ‘Steps of construction:

(i) Draw a given line Z and take any point P on it.

(ii) Draw a perpendicular line at P to the line Z such that PX = 4 cm.

(iii) Draw ∠2 = ∠1 i.e. 90° at PX and produce the line both sides.

(iv) m is the required line parallel to Z through X.

Using Properties of Alternate Angles

Question 3.

Let l be a line and P be a point not on l. Through P, draw a line m parallel to P. 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?

Solution:

Steps of Construction:

(i) Draw a line l and take any point P not on l.

(ii) Draw a line m parallel to l through P.

(iii) Join P and Q.

(iv) PQ makes ∠1 with l and ∠2 with m which are equal angles.

(v) Take any point R on m and draw ∠3 equal to ∠ 2 to meet l at S such that PQ || RS.

(vi) Since l || m and PQ || RS. Therefore, PQSR is a parallelogram.

Using the properties of parallel lines and transversal line and alternate angles