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  1. 1. TRIANGLE
  2. 2. 2634 51Which one is a triangle?
  4. 4. The types of triangles1. Types of A Triangle Based on The Length ofThe Sides2. Types of A Triangle Based on The Measuresof The Angels3. Types of A Triangle Based on The Angels andThe Sides
  5. 5. Types of Triangle Based on The Lengthof The SidesDo you still rememberabout the types oftriangle based on thelength of the sides????EquilateralTriangleIsoscelesTriangleScaleneTriangleThe types of triangle
  6. 6. Figure (a), the three sides of ΔABC have equallengths.Figure (b) on ΔDEF, length of = length of side.Figure (c), the three sides of ΔPQR have differentlengths.EF DFWhat is the resultof yourmeasurement????
  7. 7. Measure the length of three sides ofeach triangle
  8. 8. What is yourconclusion???A triangle that all of its sides are Congruent is calledas an equilateral triangleA triangle that has two congruent sides is called as anisosceles triangleA triangle that has nocongruent sides is called as ascalene triangle
  9. 9. Types of Triangle Based on TheMeasures of The AnglesDo you still rememberabout the types of trianglebased on the measures ofthe angles????Acute Triangle Right Triangle Obtuse TriangleThe types of triangle
  10. 10. The definition:A right triangle is a triangle that has one 90° angleAn acute triangle is a triangle that has three acuteanglesAn obtuse triangle is a triangle that has one obtuseangle.Do you still rememberabout the definition of eachtypes of triangle based onthe measures of theangels???
  11. 11. Based on the pictures above, which ones isright angle triangle, acute triangle andobtuse triangle????
  12. 12. Types of A Triangle Based on TheAngles and The SidesDo you still remember aboutthe types of a triangle basedon the angles and thesides????A right isoscelestriangleAn obtuseisosceles triangleAn acute isoscelestriangleThe types of triangle
  13. 13. Definition :• A right isosceles triangle is a triangle that hasone 90° angle and two equal sides.• An obtuse isosceles triangle is a triangle that hasone obtuse angle and two equal sides.• An acute isosceles triangle is a triangle that hasone acute angle and two equal sides.
  14. 14. Look at the following pictures!Which one is a right isosceles triangle, an obtuseisosceles triangle, and an acute isosceles triangle?????
  16. 16. Sum of Angles of a TriangleAttention into ABC below!What is sum of angles in the triangle? Todetermine sum of the angles, do following task.
  17. 17. Task1. Create a triangle paper ABC liked the previouspicture!2. Mark CAB with number 1. ABC with number2, and BCA with number 3. then, cut the threeangles liked the previous picture.3. Arrange the result of cutting of angles number1, 2, and 3 side by side as drawn liked previouspicture.If you do the steps above are carefully, thearrangement of the three cuts forms a straightline. Therefore CAB + ABC + BCA =180˚
  18. 18. Sum of all angles in thetriangle is 180˚
  19. 19. Mathematically, the sum of allangles in the triangle is 180˚. Byusing properties of two parallellines intersected by other line, wewill prove the value.
  20. 20. In figure beside, PQ // AB,line AR, BS, and PQ intersectat C. Based on the propertiesof two parallel line intersectedby any line, then we have thefollowings.a. ACB = SCR (due tovertical angles)b. BAC = QCR(corresponding angles)c. ABC = PCS(corresponding angles)Then, we have QCR + RCS +SCP = QCP = 180˚12321 3SP QBARC
  21. 21. ExampleDetermine the values of x, y, z ifAB // DE !Solution :See ABC! Sum of angles in ABCis 180˚.BAC + ABC + ACB = 180˚30˚ + 40˚ + ACB = 180˚ACB = 180˚- 70˚= 110˚y zx30˚C40˚A BED
  22. 22. Since ACB and DCE are vertical each other,then x = ACB = 110˚Since BCA and CED are alternate,then z = BAC = 30˚Since ABC and CDE are alternate,then y = ABC = 40˚Value of y can also be determined usingx+y+z = 180˚ (remember that sum of angularsizes in a triangles is 180˚)110˚+ y + 30˚ = 180˚y = 180˚ - 140˚ = 40˚
  23. 23. 1. Determine unknown angular sizes in following each triangle.2. Determine value of x in the following triangles.30˚(a)120˚ 35˚(c)40˚ 80˚(b)xx3x5x2xxx70˚(a) (b) (c)
  25. 25. PERIMETER OF TRIANGLE• Each plane must have perimeter.• Perimeter of any plane is sum of lengthbounding it.• So we can conclude that:Perimeter of Triangleis sum of the lengthof its sides
  26. 26. • Look at the figure• In figure beside,suppose perimeter is K• AB = c, BC = a andCA=bBC AcbaK = a+b+cHow about the Perimeter of?ABC
  27. 27. THE AREA OF TRIANGLE• Look at the figurebeside• KLMN is arectangular whereis one of itsdiagonals.LNKMNL
  28. 28. • Diagonals dividesthe rectangular into totwo congruent righttriangle, namelyand .• Since iscongruent tothen the areas of twotriangles are equalLNKLN MLNKLNMLNKMNLL KLMN = L + L= 2 x LL = x L KLMN= x KL x KNKLN2121MLNKLNKLN
  29. 29. • Look at the figure•Suppose that isright triangle in K•Line segment KL is baseof , while isaltitude of .and are right sides ofright triangle KLNKLNKLN KLKNKNK LNKLN
  30. 30. Now, look at the triangleABC in following pictureACBDA. = A. +A.= ( x AD xCD)+( x DBx CD )= x ( AD +DB ) x CD= x AB x CDABC ADC BDC21212121
  31. 31. So, we can conclude that:If the base of triangle is a ad the altitudeis t , area of triangle L is as follow.taA21
  32. 32. EXERCISEIn following figure, is aright triangle on ADetermine:a. Lb. LABCABCBCDDBCA10cm16 cm8 cm26 cm
  33. 33. Drawright, isosceles, orequilateral triangle
  34. 34. Draw right triangleSuppose we will draw a right triangle ABC. Todraw the right triangle, follow these steps.1. Draw AB2. From A, draw a perpendicular line AC withAB. The size of length is an arbitrary length(AB<AC, AB=AC, AB<AC)3. Connect C to B, so we obtain a right triangle.
  35. 35. IllustrationA BCA B A BC