properties of triangles

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Slide 1:

WELCOME TO MY MATHS PROJECT

Slide 2:

Triangles We will… …introduction to triangles …some properties of triangles …some Criteria for Congruence of Triangles …Inequalities in a Triangle

Slide 3:

Introduction To Triangles

Slide 4:

Introduction If A,B,C are three non Collinear points ,the figure made up by three line segments AB,BC and CA is called a Triangle. A triangle is a figure that has 3 sides and 3 angles. The three angles will always add up to 180 . ` Tri’ means three. A B C

Slide 5:

Find the missing angle measure? <1 = 50 ° <2= 75° <3 = ? 50 + 75 = 125 180 – 125 = 55°

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There are 4 kinds triangles by sides Right Triangle Equilateral Triangle Scalene Triangle Isosceles Triangle

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There are 4 kinds triangles by angles Acute Obtuse Right Equilateral

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Properties Of Triangles

Angle sum property of a Triangle:

Angle sum property of a Triangle The sum of the angles of a triangle is 180˚. A B C B C A

Angle sum property of a Triangle:

Angle sum property of a Triangle 1 2 3 4 5 Angle 4 + Angle 3 + Angle 5=180º Angle 1 + Angle 3 + Angle 2=180º

Exterior & Interior Opposite Angles:

Exterior & Interior Opposite Angles A B C D

Exterior angle property of a Triangle:

Exterior angle property of a Triangle A B D C Angle A + Angle B = Angle BCD

Exterior angle property of a Triangle:

Exterior angle property of a Triangle A B D C Angle A + Angle B + Angle BCA=180º Angle BCA + Angle BCD=180º Angle A + Angle B +Angle BCA = Angle BCA+ Angle BCD

Slide 15:

Inequalities in a Triangle

Triangle Inequality Property:

Triangle Inequality Property The sum of any two sides of a triangle is greater than the third side. A B C AB+BC >AC AB+AC>BC AC+BC>AB

Triangle Inequality Property:

Triangle Inequality Property A B C AB+BC >AC

Triangle Inequality Property:

Triangle Inequality Property A B C AB+AC>BC

Triangle Inequality Property:

Triangle Inequality Property A B C AC+BC>AB

Pythagoras Theorem:

Pythagoras Theorem In a right triangle, the square of the longest side is equal to the sum of squares of remaining two sides. A B C ( AC) 2 = (AB) 2 + (BC) 2 Hypotenuse 2 = Perpendicular 2 + Base 2 Base Perpendicular Hypotenuse

Pythagoras Theorem:

Pythagoras Theorem

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Criteria for Congruence of Triangles

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Definition of Congruent Triangles (CPCTC) Two triangles are congruent if and only if their corresponding parts are congruent. CPCTC C orresponding P arts of C ongruent T riangles are C ongruent

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SAS congruence rule : Two triangle are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle. C ongruence rule of Triangles ASA congruence rule: Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle.

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Thanks for watching My presentation Presented by- Mohini Mathur IX-A VISIT HERE- www.mohinimathur.com

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