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TRIANGLE

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PREPARED BY

MANINDER PAL SINGH

TGT MATHS

JNV BANSWARA II

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INTRODUCTION

*A Triangle is a simple closed curve made up of three line segments.

* A Triangle has 6 elements i.e. 3 sides and 3 angles.

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  • Triangle ABC denoted as Δ ABC. Where AB, BC , CA are three sides and A,B, C are three angles

A

B

C

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TYPES OF TRIANGLES

On the Basis of length of sides , there are 3 types of Triangles.

Equilateral Triangle : 3 Sides are equal

Isosceles Triangle : 2 Sides are equal

Scalene Triangle : No side equal

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On the Basis of Angles, there are 3 types of Triangles.

Acute Angle Triangle : 3 Angles < 90°

Obtuse Angle Triangle : 1 Angle > 90° but <180°

Right Angle Triangle : 1 Angle = 90°

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MEDIAN OF TRIANGLE

*A line segment joining a vertex to mid point of opposite side is called median of triangle .

*In fig. AD,BE and CF are the Medians of Triangle.

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A

B

C

D

E

F

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CONGRUENT

*If two Geometrical figures coincides exactly , by placing one over the other, then these figures are said to be congruent to each other.

* Congruent means equal in all respect or figures whose shape and size are both the same.

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CRITERIAS FOR CONGRUENCE OF TWO TRIANGLES

*SAS ( SIDE–ANGLE-SIDE) Congruence

*ASA (ANGLE–SIDE–ANGLE)Congruence

*AAS (ANGLE–ANGLE–SIDE)Congruence

*SSS(SIDE–SIDE–SIDE)Congruence

*RHS (Right an -Hypotenuse-Side)Congruence

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SAS CONGRUENCE

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NOW IF, AB = PQ

Angle B = Angle Q

BC = QR

Then ΔABC CONGRUENT TO ΔPQR

B

A

C

P

Q

R

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SUMMARY

  1. Two figures are congruent , if they are of the same shape and size.
  2. If two sides and the included angle of one triangle is equal to the two sides and included angle of another triangle then these triangle are congrent.
  3. If two angles and the included side of one triangle are equal to the two angle and the included side of other triangle then the two triangles are congruent .
  4. If two angle and the one side of one triangle is equal to the two angle and the corresponding side of other triangle then the two triangles are congruent .
  5. If three sides of a triangle is equal to the three sides of other triangle then the two triangles are congruent .
  6. If in two right angled triangle , Hypotenuse and one side of the triangle are equal to Hypotenuse and one side of the other triangle then the two triangle are congruent.

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THANKS