Triangle B 2
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NAM E OF TH E SC HOO L
GOVT. SE C SCHOOL .BOYS. NABHA
NA ME OF THE PROJ ECT
CONSTRUCTION AND PROPERTIES OF A TRIANGLE
INDEX INTRODUCTION OF TRIANGLE TYPES OF TRIANGLE ARC LINE ANGLE PROBLEM PROPERTIES OF TYRIANGLE
TRIANGLE:
A geometric figure consisting of three points, called vertices, connected by three sides. C
A
B
TYPES OF TRIANGLES:
Types of Triangles Triangles are classified in terms of their sides and angles. Scalene triangles have no equal sides (fig. 1), isosceles triangles have two equal sides (fig. 4), and equilateral triangles have three equal sides (fig. 5). In acute triangles, all the angles are less than 90° (fig. 1). In right triangles, one angle is equal to 90° (fig. 3). In obtuse triangles, one angle is more than 90° (fig. 2).
LINE:
Line (geometry), a series of adjacent points that extends to infinity in two directions.
A
B
ARC:
Arc (mathematics), in mathematics, a segment of a continuous curve.
ANGLE:
Angle (geometry), a measure of the rotation of a line segment about a fixed point.
PROBLEM TO BE SOLVED
To Construct a Triangle ABC whose perimeter is 11.5cm and base angles are 60 and 90 Given:-A triangle ABC whose perimeter is 11.5cm and base angles are 60 and 90.
Points of construct:
Step1.Draw a line of any length.
Step2.Take a line segment ON=11.5cm from the line drawn.
O
N
Step3.Construct XON=900 and ONY=600 X Y
90 60 O
N
Step4.Draw Bisectors of ONY and NOX meeting at a point C. Y
X C
90 60 O
N
Step5.Draw the perpendicular bisectors of OC and NC intersecting ON at A and B respectively. Y
X C
90 O
60 N A
B
Step6.Join C to B and A. Y
X C
60
90 O
N A
B
In this way, ABC is our required triangle.
Y
X C
60
90
O
A
B
N
PROPERTIES OF TRIANGLES
If one angle of a triangle is equal to one angle of the other and the sides including these angles are proportional ,the triangles are similar. If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse ,the triangles on each side of the perpendicular are similar to the whole triangle and to each other. The internal bisector of an angle of a triangle divides the opposite sides in the ratio of the sides containing the angle .
CREATED BY: CLASS: 9TH GURVINDER SINGH GURDEEP SINGH AND CLASS
GUIDED BY:
S. PARMJEET SINGH [M.A.Eco.B.Sc.B.Ed.] (MATHS TEACHER)
Mr. Parminder Singh (Student Trainer) M. Sc. (IT) GOVT SEC SCHOOL NABHA (FOR BOYS).
GOVT. SE C SCHOOL .BOYS. NABHA
NA ME OF THE PROJ ECT
CONSTRUCTION AND PROPERTIES OF A TRIANGLE
INDEX INTRODUCTION OF TRIANGLE TYPES OF TRIANGLE ARC LINE ANGLE PROBLEM PROPERTIES OF TYRIANGLE
TRIANGLE:
A geometric figure consisting of three points, called vertices, connected by three sides. C
A
B
TYPES OF TRIANGLES:
Types of Triangles Triangles are classified in terms of their sides and angles. Scalene triangles have no equal sides (fig. 1), isosceles triangles have two equal sides (fig. 4), and equilateral triangles have three equal sides (fig. 5). In acute triangles, all the angles are less than 90° (fig. 1). In right triangles, one angle is equal to 90° (fig. 3). In obtuse triangles, one angle is more than 90° (fig. 2).
LINE:
Line (geometry), a series of adjacent points that extends to infinity in two directions.
A
B
ARC:
Arc (mathematics), in mathematics, a segment of a continuous curve.
ANGLE:
Angle (geometry), a measure of the rotation of a line segment about a fixed point.
PROBLEM TO BE SOLVED
To Construct a Triangle ABC whose perimeter is 11.5cm and base angles are 60 and 90 Given:-A triangle ABC whose perimeter is 11.5cm and base angles are 60 and 90.
Points of construct:
Step1.Draw a line of any length.
Step2.Take a line segment ON=11.5cm from the line drawn.
O
N
Step3.Construct XON=900 and ONY=600 X Y
90 60 O
N
Step4.Draw Bisectors of ONY and NOX meeting at a point C. Y
X C
90 60 O
N
Step5.Draw the perpendicular bisectors of OC and NC intersecting ON at A and B respectively. Y
X C
90 O
60 N A
B
Step6.Join C to B and A. Y
X C
60
90 O
N A
B
In this way, ABC is our required triangle.
Y
X C
60
90
O
A
B
N
PROPERTIES OF TRIANGLES
If one angle of a triangle is equal to one angle of the other and the sides including these angles are proportional ,the triangles are similar. If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse ,the triangles on each side of the perpendicular are similar to the whole triangle and to each other. The internal bisector of an angle of a triangle divides the opposite sides in the ratio of the sides containing the angle .
CREATED BY: CLASS: 9TH GURVINDER SINGH GURDEEP SINGH AND CLASS
GUIDED BY:
S. PARMJEET SINGH [M.A.Eco.B.Sc.B.Ed.] (MATHS TEACHER)
Mr. Parminder Singh (Student Trainer) M. Sc. (IT) GOVT SEC SCHOOL NABHA (FOR BOYS).
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