# Constructions Class 10 Notes Maths Chapter 11

#### 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.

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