Triangles srini ppt
- 1. SRI ADICHUNCHANAGIRI COLLEGE OF EDUCATION CHANNARAYAPATANA SUBJECT : MATHEMATICS TOPIC : TRIANGLES BY SRINIVASA
- 2. TRIANGLES
- 3. OBJECTIVES IN THIS LESSON 1) DEFINE THE CONGRUENCE OF TRIANGLE. 2)STATE THE CRITERIA FOR THE CONGRUENCE OF TWO TRIANGLES. 3)SOME PROPERTIES OF A TRIANGLE. 4)INEQUALITIES IN A TRIANGLE.
- 4. INTRODUCTION • We know that a closed figure formed by three intersecting lines is called a triangle(‘Tri’ means ‘three’).A triangle has three sides, three angles and three vertices. For e.g. In Triangle ABC, denoted as ∆ABC AB,BC,CA are the three sides, ∠A,∠B,∠Care three angles and A,B,C are three vertices. A B C
- 5. DEFINING THE CONGRUENCE OF TRIANGLE:- • Let us take ∆ABC and ∆XYZ such that corresponding angles are equal and corresponding sides are equal CORRESPONDING PARTS A ∠A=∠X X ∠B=∠Y ∠C=∠Z AB=XY BC=YZ B C AC=XZ Y Z
- 6. This also means that:- • A corresponds to X • B corresponds to Y • C corresponds to Z For any two congruent triangles thecorresponding parts are equal and are termed as CPCT – Corresponding Parts of Congruent Triangles
- 7. PROPERTIES OF TRIANGLE A B C A Triangle in which two sides are equal in length is called ISOSCELES TRIANGLE. So, ∆ABC is a isosceles triangle with AB = BC.
- 8. Inequalities in a Triangle • Theorem on inequalities in a triangle If two sides of a triangle are unequal, the angle opposite to the longer sideis larger ( or greater) 109 8 Here, by comparing we will get that Angle opposite to the longer side(10) is greater(i.e. 90°)
- 9. In any triangle, the side opposite to the longer angle islonger. 109 8 Here, by comparing we will get that Side(i.e. 10)opposite to longer angle (90°) is longer.
- 10. The sum of any two side of a triangle is greater than thethird side. 109 8 Here by comparing we get- 9+8>10 8+10>9 10+9>8 So, sum of any two sides is greater than the third side.
- 11. 1.Two figures are congruent, if they are of the same shape andsize. 2.If two sides and the included angle of one triangle is equal to the two sides and the included angle then the two triangles are congruent(by SAS). 3.Angles opposite to equal sides of a triangle are equal. 4.Sides opposite to equal angles of a triangle. areequal. 5.Each angle of equilateral triangle are 60°. 6.In a triangle, angles opposite to thelonger side is larger. 7.In a triangle, side opposite to the larger angle is longer. 8.Sum of any two sides of triangle is greater than the thirdside. SUMMARY
- 13. Questions 1) What is triangle? 2) What is Isosceles Triangle ? 3) What is CPCT ? 4) Properties of triangle ?