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**Practical Geometry**

**10.1 INTRODUCTION**

You are familiar with a number of shapes. You learnt how to draw some of them in the earlier classes. For example, you can draw a line segment of given length, a line perpendicular to agiven line segment, an angle, an angle bisector, a circle etc. Now, you will learn how to draw parallel lines and some types of triangles.

**10.2 CONSTRUCTION OF A LINE PARALLEL TO A GIVEN LINE,THROUGH A POINT NOT ON THE LINE**

Let us begin with an activity (Fig 10.1)

(i) Take a sheet of paper. Make a fold. This fold represents a line l.

(ii) Unfold the paper. Mark a point A on the paper outside l.

(iii) Fold the paper perpendicular to the line such that this perpendicular passes through A. Name the perpendicular AN.

(iv) Make a fold perpendicular to this perpendicular through the point A. Name the new perpendicular line as m. Now, l || m. Do you see ‘why’?Which property or properties of parallel lines can help you here to say that lines l and m are parallel.

You can use any one of the properties regarding the transversal and parallel lines to make this construction using ruler and compasses only.

**Step 1 Take a line ‘l ’ and a point ‘A’ outside ‘l ’ [Fig10.2 (i)].**

**Step 2 Take any point B on l and join B to A [Fig 10.2(ii)].**

**Step 3 With B as centre and a convenient radius, draw an arc cutting l at C and BA at D [Fig 10.2(iii)].**

**Step 4 Now with A as centre and the same radius as in Step 3, draw an arc EF cutting AB at G [Fig 10.2 (iv)]**

**Step 5 Place the pointed tip of the compasses at C and adjust the opening so that the pencil tip is at D [Fig 10.2 (v)].**

**Step 6 With the same opening as in Step 5 and with G as centre, draw an arc cutting the arc EF at H [Fig 10.2 (vi)].**

**Step 7 Now, join AH to draw a line ‘m’ [Fig 10.2 (vii)].**

**Note that ∠ABC and ∠BAH are alternate interior angles. Therefore m|| l**

**Please refer to attached file for NCERT Class 7 Maths Practical Geometry**