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Triangles1.

What are triangles ?? ??1.

A Triangle is a 3-sided polygon. Every

triangle has three sides, three vertices and

three angles. All triangles are convex and

bicentric. That portion of the plane

enclosed by the triangle is called the

triangle interior while the remainder is the

exterior.

Types of Triangles

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On Basis of Length of Sides, there are 3 types of Triangles• Equilateral Triangle• Isosceles Triangle• Scalene Triangle

On Basis of Angles, there are 3 types of triangles • Acute Angled Triangle• Obtuse Angled Triangle• Right Angled Triangle

TYPES OF TRIANGLES

Properties

OFA Triangle.

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Properties

Pythagorus theoram

Exterior angle

property

Angle sum property

• Angle sum property-Angle sum Property of a Triangle is that the sum of all interior angles ofa Triangle is equal to 180˚.

• Exterior angle property-Exterior angle Property of a Triangle is that An exterior angle of theTriangle is equal to sum of two opposite interior angles of the Triangle

• Pythagorus theoram-Pythagoras Theorem is a theorem given by Pythagoras. The theorem isthat In a Right Angled Triangle the square of the hypotenuse is equal tothe sum of squares of the rest of the two sides.

Properties of an isosceles triangle

• Angle opposite to the equal sides of an isosceles triangle are equal.

• The sides opposite to the equal angles of a triangle are equal.

Secondary Parts

OF ATriangle.

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Median of a triangle1. The Line Segment joining the midpoint of the base of the Triangle is called Median of the Triangle.

OR

2. A Line Segment which connects a vertex of a Triangle to themidpoint of the opposite side is called Median of the Triangle.

MEDIAN

Altitudes of a triangleThe Line Segment drawn from a Vertex of a Triangle perpendicular to its opposite side is called an Altitude or Height of a Triangle.

ALTITUDE

Perpendicular bisector

A line that passes through midpoint of thetriangle or the line which bisects the third side of thetriangle and is perpendicular to it is called thePerpendicular Bisector of that Triangle.

Perpendicular Bisector

Angle Bisector

A line segment that bisects an angle of a triangleIs called Angle Bisector of the triangle.

ANGLE BISECTOR

Congruency OF A Triangles

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•Two figures are congruent, if they are of the same shape and of the same size.

•Two circles of the same radii are congruent.

•Two squares of the same sides are congruent.

SSS criteria of congruency

If the three sides of one Triangle are equal to the three sides of another Triangle. Then the triangles are congruent by the SSS criteria.

SSS criteria is called Side-Side-Side criteria of congruency.

SAS criteria of congruency

If two sides and the angle included between them is equal to the corresponding two sides and the angle between them of another triangle. Then the both triangles are congruent by SAS criteria i.e. Side-Angle-Side Criteria of Congruency.

ASA criteria of congruency

If two angles and a side of a Triangle isequal to the corresponding two anglesand a side of the another triangle thenthe triangles are congruent by the ASACriteria i.e. Angle Side-Angle Criteria ofCongruency.

AAS criteria of congruency

If two angles and one side of onetriangle are equal to angles to twoangles and the corresponding side ofthe other triangle then the two trianglesare congruent

RHS criteria of congruency

If the hypotenuse, and a leg of one rightangled triangle is equal to correspondinghypotenuse and the leg of another rightangled triangle then the both triangles arecongruent by the RHS criteria i.e. RightAngle-Hypotenuse-Side Criteria ofCongruency.

Inequalities

INA Triangle.

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• In a triangle ,angle opposite to the longer side is larger.

• In a triangle, side opposite to the larger(greater) angle is longer.

• Sum of any two sides of a triangle is greater than the third side.

• Difference of any two sides of a triangle is smaller than the third side.

SomeUnknown

Facts About Triangles.

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Centres of a circle

• Incentre- The three angle bisectors of a triangle meet in

one point called the incentre. It is the centre of the incircle, the circle inscribed by the triangle

• Circumcentre- Three perpendicular bisectors of the sides of

the triangle meet in one point called circumcentre. It is the centre of the circumcircle, the circle circumscribed about the circle.

• Centroid- The three medians meet in the centroid of the

centre or center of the mass(centre of gravity).

• Orthocentre-The three altitudes of a tiangle meet in onepoint called the orthocentre.

PYTHAGORAS EUCLID PASCAL

MATHEMATICIANS RELATED TO TRIANGLES

GUNNEEK,ARSDEEP,NIDHI &ANJALI