Presentation By Tushar Chandrakant Mhatre Asst Teacher Shri

Presentation By Tushar Chandrakant Mhatre (Asst. Teacher) Shri Chhatrapati Shivaji Highschool and Loknete D. B. Patil junior college Jasai

Unit 3 : Geometric Constructions Sub. Units Revision of basic construction. To construct the circumcircle and incircle of a triangle. Construction of a tangent to the circle. To construct an are in-scribing an angle of given measure. Construction of triangle. The construction of similar Triangles.

2) Draw perpendicular 3. 2 a) To construct the bisectors of any two sides. circumcircle of a triangle. Let 'O' be the point of Illustration Ex. intersection. Draw the circumcircle of A DEF in which DE = 5. 2 cm, D = 500, E = 750 Steps of construction Construct . DEF 1) Construct . DEF 3) Draw a circle with centre O and radius OD/OE/OF.

b) To construct incircle of a triangle. Illustration Ex. Draw the incircle of XYZ such that XY=6. 1 cm ZY=5. 7 cm and ZXYZ=650 Steps of construction 3) Draw a circle 2) Draw the bisectors of with the radius MI 1) Construct . XYZ; Y and X. Let these and Centre at I. bisectors intesect at with given point I. Draw a measuremnts. perpendicular. IM on side XY. Point M is the foot of the perpendicular.

3. 3) Construction of a tangent to the circle. A) Construct the tangent to a circle at a point on the circle. Illustration. Ex. To construct a tangent to a circle of radius 3. 2 cm at a point on it. 1) Draw a circle with centre O and radius 3. 2 cm. 2) Take any point 'P' on the circle and draw ray OP. 3) Draw a line perpendicular to ray OP at the point P. Name that line as 'l' which is tangent to the circle.

b) Construct of a tangent to the circle (without using centre of the circle) Recall the property of angles in alternate segments. Illustration : Ex. : Draw a circle of radius 3. 5 cm, take any point K on it. Draw a tangent to the circle at K without using centre of the circle. 2) Take any 1) Draw a circle of radius 3. 5 cm. Take any point K on it draw the chord KL of any length. point M on the alternate are of KXL other than K and L. Joint MK and LM. So LMK is formed. 3) Draw ray KN making an angle equal to LMK using KL as one side and vertex K.

c) To draw tangent to a circle from a point outside the circle. We have studied that, "The angle inscribed in a semi circle is a right angle. " We shall use this property to draw a tangent to a circle from a point outside the circle. Illustration. Ex. Construct tangents to the circle of radius 2. 8 cm. from a point at a distance 6. 5 cm. from the centre. 1) Construct a circle with centre O and radius 2. 8 cm. Take point P such that OP=6. 5 cm. 2) Obtain midpoint M of seg OP. Draw a circle with centre M and radius MP. 3) Let A and B be the points of intersection of these two circles.

3. 5) Construction of triangle : a) To construct a triangle with a given base, vertex angle and a median corresponding to the base : b) To construct a triangle with a given base, altitude and the angle opposite to the base : -

3. 6) The construction of Similar Triangles. For a given one-to-one correspondence between the vertices of two triangles if their corresponding angles are congruent and corresponding sides are in a proportion then. These two triangles are called 'Similar Triangles' Use these property we will construct Similar triangle. Illustration : Ex. 1 ABC PQR, in ABC, AB=3. 6 cm, BC=4 cm and AC=4. 2 cm. The corresponding sides of ABC and PQR are in the ratio 2: 3, construct PQR. Solution : ABC PQR

Ex. 2 RKN SPV, in RKN, RK=6. 4 cm, R=600, K=500 and RN/SV=4/3 ; then construct triangles. Solution RKN SPV

Ex: ∆ PSE ~ ∆ TSV ; In ∆ PSE, PS = 4. 4 cm, SE = 5. 1 cm PE = 5. 5 cm and PS = 5. construct ∆ TSV TS = 3 1)Draw ∆ SPE, Draw a Suitable < PST on ray SX take 5 equal parts. SS 1, S 1 S 2, S 2 S 3, S 3 S 4, S 5. Join Pointsx

2) Join PS 5, and measure < PS 5 S. Draw Same angle < SS 3 T (Points T on seq SP ) 3) Join Seq V. T ∆ PSE, is given We get ∆ TSV, Similar to ∆ PSE. …∆ PSE ~ ∆ TSV

Ex. 3 LMN LQP, In LMN, LM=3. 6 cm, L=500 LN=4. 2 cm. and LM/LQ=4/7 Construct LQP.

riangle Examplea: - Construct and 5 cm draw a triangle ABCSimilar to Triangle ABC, each of whose side is 2 of the corresponding Sides of triangle ABC. 3

2 construct a triangle ABC whose side are 8 cm, 7 cm 6 cm construct another triangle to triangle ∆ ABC. with side 2 of the corresponding Sides of triangle ABC. 3