Triangle and its properties
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This presentation discusses properties of triangles, including: - Classifying triangles by side lengths as scalene, isosceles, or equilateral. - Classifying triangles by angle measures as acute, obtuse, or right. - Defining medians and altitudes of triangles. - Proving properties such as the angle sum theorem, the exterior angle theorem, and Pythagorean theorem.
Triangle and its properties
- 1. PRESENTATION ON THETRIANGLE AND ITS PROPERTIES
- 2. The Triangle and its Properties •Triangle •Triangle . .
- 3. Based on the sides Scalene Triangles Isosceles Triangles Equilateral Triangles Classification of triangles Scalene Isosceles Equilateral
- 4. Classification of triangles Based on Angles Acute-angled Triangle Obtuse-angled Triangle ° Right-angled triangles Acute Triangle Right Triangle Obtuse Triangle
- 5. MEDIANS OF A TRIANGLE
- 6. ALTITUDES OF A TRIANGLE • Altitude – line segment from a vertex that intersects the opposite side at a right angle. Any triangle has three altitudes.
- 7. ACUTE OBTUSE B A C ALTITUDES OF A TRIANGLE
- 8. Proof: C + D + E = 1800 ……..Straight line A = D and B = E….Alternate angles C + B + A = 1800 A + B + C = 1800 D E Given: Triangle A B C Construction: Draw line ‘l’ through C parallel to the base AB The measure of the three angles of a triangle sum to 1800 . To Prove : A + B + C = 1800 l ANGLE SUM PROPERTY OF A TRIANGLE
- 9. An exterior angle of a triangle equals the sum of the two interior opposite angles in measure. To Prove: ACD = ABC + BAC Proof: CB + ACD = 1800 …………………. Straight line ABC + ACB + BAC = 1800 …………………sum of the triangle ACB + ACD = ABC + ACB + BAC ACD = ABC + BAC A B C D Given: In Δ ABC extend BC to D EXTERIOR ANGLE OF A TRIANGLE AND ITS PROPERTY
- 10. PYTHAGORAS THEOREM In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. In ABC : • AC is the hypotenuse • AB and BC are the 2 sides Then according to Pythagoras theorem , A B C AC² = AB² + BC²