Maths Chawinda Devi Amritsar

CONSTRUCTION OF TRIANGLES (a) Construction of scalene triangle •

To construct a triangle when lengths of its three sides are given. let the lengths of three sides be 3.7 cm, 4.0 cm and 5.6 cm.

Steps Draw AB = 3.7 cm. With A as center and radius = 4.0 cm, draw an arc. With B as center and radius = 5.6 cm, draw one more arc which cuts the former arc at C. Join AC and BC. ABC is the required triangle.

C

5.6 cm

4 cm

A

3.7 cm

B

(B) To construct a triangle when lengths of two of its sides and the included angle are given. Let the lengths of two sides be 4.0 cm and 3.6 cm; and the included angle be 450.

Steps :Draw AB = 4.0 cm. Draw AP, making angle 450 with AB i.e. PAB = 450. From AP, Cut AC = 3.6 cm. Join B and C. ABC is the required triangle.

C

3.6 cm

A

4.0 cm

B

© To construct a triangle when two angles and the length of one side be 4.5 cm.

Let the angles be 45o. and 60o and the length of one side be 4.5 cm.

STEPS :Draw BC = 4.5 cm. Draw BP, making angle 450 with BC. Draw CQ, making angle 600 with BC. Let BP and CQ intersect at A. ABC is the required triangle.

Q

A

45O B

P

60O 4.5 cm

C

(D) To construct a right angled triangle when lengths of its hypotenuse and one side are given. Let the hypotenuse and ones side are given.

STEPS :Draw BC = 4.5 cm. Draw BP, making angle 900 with BC. With C as center and radius = 6cm, draw an arc which cuts BP at A. Join A and C. ABC is the required triangle.

P A

6 cm

B 4.5 cm

C

(B) Construction of Isosceles triangle •

To construct an isosceles triangle when its base and one base angle are given. Since base angles of an isosceles triangle are equal; therefore, to construct the required triangle, use the same method as used in constructing the triangle having having two angles and the included side.

2. To construct an isosceles triangle when its base and altitude are given Let the base= 6 cm and altitude = 3.2 cm. Steps:Draw BC= 6 cm. Draw PQ, which cuts BC at O. From OP cut OA = 3.2 cm Join AB and AC.

P A

B

O

Q

C

3. To construct an isosceles triangle when its altitude and angle at the vertex are given Let the altitude be= 4.0 cm and angle at the vertex = 60o Steps:• Draw a line PQ of any suitable length. • Through a point O in PQ, draw OA perpendicular to PQ such that OA=4.0 cm • Through A, draw AB and AC, on the opposite sides of OA and making angle = 60o with it, meeting PQ at B and C.

A

P

B

O

C

Q

Construction of Equilateral triangle •

To construct an equilateral triangle when one side is given. Since sides of an equilateral triangle are equal, therefore , to construct the required triangle use the same method as used to construct a triangle whose all three sides are given.

2. To construct an isosceles triangle when its altitude and angle at the vertex are given Let the altitude of the required equilateral triangle be= 4.0 cm. Steps:Draw a line PQ of any suitable length. Through a point O in PQ, draw OA perpendicular to PQ such that OA=4.0 cm Through A, draw AB and AC, making angles equal to 30o each with OA and meeting PQ at B and C.

A

P

B

O

C

Q

• If one side of the triangle is produced the exterior angle so formed is greater than each of the interior opposite angles. • A triangle cannot have more than one right angle. • A triangle cannot have more than one obtuse angle.

Contd... 4. In a right angled triangle the sum of the two acute angle is 90o . 5. In every triangle at least two angles are acute. 6. If two angles of a triangle are equal to two angles of any other triangle each to each, then the third angle of the both triangles are also equal.

PREPARED BY :KOMALPRET KAUR RAZIA PARDEEP KAUR AKHWINDER KAUR RANJIT KAUR CLASS X A

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