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°
Slide 6: There are 4 kinds triangles by sides Right Triangle Equilateral Triangle Scalene Triangle Isosceles Triangle
Slide 7: There are 4 kinds triangles by angles Acute Obtuse Right Equilateral
Slide 9: 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
Slide 22: Criteria for Congruence of Triangles
Slide 23: 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
Slide 24: 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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Slide 26: Thanks for watching My presentation Presented by- Mohini Mathur IX-A VISIT HERE- www.mohinimathur.com