Construction And Properties Of Triangle(nehru Garden)

CONSTRUCTION AND PROPERTIES OF TRIANGLE PRESENTED BY: Govt. Girls Sr. Sec. School NEHRU GARDEN,JALANDHAR

What is a triangle A closed figure obtained by joining three non-collinear point is called triangle. A triangle ABC has been shown in figure .here A,B and C are the vertices of the Triangle ABC and the line segment AB,BC,CA are the Sides Of the Triangle. Also BAC, B ABC , BCA are the angles of triangle ABC .We can write these angles as A , B, C

A

Angle C Side

Vertex

Properties of triangle 1. Sum of the angles of a triangle is 1800. Proof: Proof 1.Draw a triangle and label its angles as 1,2 and 3 2. Cut out the triangular region into three parts. 1 2

3

Sum of the angles of a triangle is 1800. 3. Draw a line POQ on a sheet of paper and arrange the cut out angles on it so that vertex of each is at O. We can observe that the three angles together makes up a straight angle POQ and a straight angle is of 1800

2 3

1 P

O

Q

equal to the sum of two interior opposite angles. Proof :1 Draw a triangle ABC with exterior angle ACD and label interior able opposite to this exterior angle as 1 and 2 2. cut out these angles and arrange the interior angle 1 and 2 over exterior angle ACD 3. We will find that these angle will cover the exterior angle completely.

equal to the sum of two interior opposite angles A

A

1

1

2 B

C

D

C

2 D

3. The sum of sides of a triangle is greater than the third side Proof : To prove this property we draw three triangles ABC and find the length of side AB,BC,CA in each triangle and collected the following information. Triangle

Side Side Side Is AB+BC AB BC AC > CA ?

Is BC+CA > AB ?

Is CA+AB > BC ?

1

4cm

9cm

7cm

4+9>7

9+7>4

7+4>9

2

2cm

3cm

4cm

2+3>4

3+4>2

4+2>3

3

3cm

4cm

5cm

3+4>5

4+5>3

5+3>4

Construction of triangle Here we are presenting the construction of the triangle whose Two sides and one angle is given. To make such kind of triangle firstly we will draw a rough sketch of the triangle and then go with the actual construction .

Construction of triangle with one angle and two side Draw the rough sketch in with draw one of the side as base side BC and angle indicated at any of vertex then cut this angle line to the length of second side and join the intersection point with other vertex .

Construction of triangle in which AB=4cm, BC=5cm and B=450 A

Steps of Construction

4cm

1. Draw rough sketch as

45 B

0

5cm

C

2. Draw Base line BC=5cm with the help of scale.

B

5cm

C

Construction of triangle in which AB=4cm, BC=5cm and B=450 3. Make angle of 450 on vertex B with the help of protractor. X

450 B

5cm

C

Construction of triangle in which AB=4cm, BC=5cm and B=450 4. Place start point of the scale at point B and mark a point on line BX at 4cm distance and named this point as A. X A 4cm 450 B

5cm

C

Construction of triangle in which AB=4cm, BC=5cm and B=450 5. Join point A with Vertex C .Triangle ABC is the required triangle. X A 4cm 450 B

5cm

C

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