#### CHAPTER AT A GLANCE

**Construction**

Construction implies drawing geometrical figures accurately such that triangles, quadrilateral and circles with the help of ruler and compass.

**Division of a Line Segment**

A line segment can be divided in a given ratio (both internally and externally)

**Example:**

Divide a line segment of length 12 cm internally in the ratio 3 : 2.

**Solution:**

Steps of construction :

(i) Draw a line segment AB= 12 cm. by using a ruler.

(ii) Draw a ray making a suitable acute angle LBAX with AB.

**(iii)** Along AX, draw 5 ( = 3 + 2) arcs intersecting the rayAX atA1,A2 ,A3,A4 and A5 such that AA1 = A1A2 = A2A3 = A3A4 = A4A5**(iv)** Join BA5.**(v)** Through A3 draw a line A3P parallel to A5B making LAA3P = LAA5B,

intersecting AB at point P.

The point P so obtained is the required point, which divides AB internally in the ratio 3 : 2.

**Similar Triangles**

(i) This Construction involves two different situation.

- (a) Construction of a similar triangle smaller than the given triangle.
- (b) Construction of a similar triangle greater than the given triangle.

(ii)The ratio of sides of the triangle to be constructed with the corresponding sides of the given triangle is called scale factor.

**Example:**

Draw a triangle ABC with side BC= 7 cm. LB= 45°, LA= 105°. Construct a triangle whose sides are (4/3) times the corresponding side of ABC.

**Tangents to a Circle**

Two tangents can be drawn to a given circle from a point outside it.

**Example:**

Draw a circle of radius 4 cm. Take a point P outside the circle. Without using the

centre of the circle, draw two tangents to the circle from point P.

**Note:** If centre of a circle is not given,then it can be located by finding point of intersection of perpendicular bisector,of any two non-parallel chords of a circle.

**Related Articles:**

- Class 10 Notes
- CBSE Class 10 Maths Notes
- NCERT Solutions for class 10th Maths Chapter 11 Constructions