**Chapter
10 Practical Geometry**

**Exercise
10.1**

Ex 10.1 Class 7 Maths 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

(v) MN is the required line.

Using the Property of Alternate Angles

**Ex 10.1 Class 7
Maths 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

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

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

Using Properties of Alternate Angles

**Ex 10.1 Class 7
Maths 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

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

(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

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

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

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