•   Created By:•   Yola Yaneta H.•   Nurina Ayuningtyas•   Wahyu Fajar S.•   Yan Aditya P.
UADRILATERAL….?It is a geometrical shape havingexactly 4 sides. quad means fourand lateral means side .
IND THE QUADRILATERALS IN THE FOLLOWINGPICTURES…!
   A square is a quadrilateral where all sides    are equal in length and all angles are equal.
QUARE it has four equal sides and four equal angles (90  degree angles, or right angles) The diagonals of a square bisec...
RECTANGLE   Rectangle is a quadrilateral whose opposite sides    in the same length and the angles are equal.
ECTANGLE• any quadrilateral with four right angles.• Opposite sides are parallel and congruent.• The diagonals bisect each...
PARALLELOGRAM  A parallelogram is a quadrilateral in which the opposite  sides are parallel.
ARALLELOGRAM   Opposite sides are parallel and equal in length   and opposite angles are equal (angles "a" are the same,...
RHOMBUS
HOMBUS A four-sided shape where all sides have equal  length. opposite sides are parallel opposite angles are equal. t...
RAPEZOIDA trapezoid has one pair of opposite sidesparallel.
Isosceles trapezoid : if the sides that arent parallel are equal in lengthand both angles coming from a parallel side are ...
he Kite  Kites are quadrilaterals with exactly two distinct pairs  of adjacent are equal length.
he Kite The diagonals of a kite are perpendicular. Exactly one pair of opposite angles are congruent.
   How to find Perimeter???           A perimeter is a path that surrounds an area, so we           just add all of the s...
   Perimeter square ABCD. AB= 3 cm               Perimeter ABCD= 3+3+3+3 = 12 cm   Perimeter Rhombus ABCD. AB=4 cm     ...
DEFINE AREASQuadrilateral
SQUAREWhat is the area   H=heightof this SQUARE?W=width
RECTANGLE7   14 21 28 35 42 496   13 20 27 34 41 485   12 19 26 33 40 47      What is the area     H=height4   11 18 25 32...
RECTANGLE765        What is the area     H=height4        of this rectangle?321   8     15 22 29 36 43             W=width
RECTANGLEWhat is the area     H=heightof this rectangle?W=width
RECTANGLE7   14 21 28 35 42 49 56 636   13 20 27 34 41 48 55 625   12 19 26 33 40 47 54 61         What is the area   H=he...
RECTANGLE765            What is the area             H=height4            of this rectangle?321   2   3      4    5   6   ...
RECTANGLE765            What is the area             H=height4            of this rectangle?321   2   3      4    5   6   ...
RECTANGLE76             Arearectangle5        = What is the area          Rows x Columns                 H=height4        ...
PARALELOGRAM The length is m and the height is n Cut the height, and move it in the rights side. So we get rectangle no...
     Given diagonal a=6cm and diagonal b=4cm. Draw                into 2 rhombus.               Cut rhombus A into 4 equ...
     Given diagonal a=9cm and diagonal b=4cm.              Draw into 2 kites.             Cut kites A into 4 equal parts...
TRAPEZOID   Trapezoid with upper=a, base=b, height=h   Make it again with same trapezoid and flip it.   Cut the triangl...
TRIANGLE           Phee.radhieanz@gmail.com
TrianglesShapes with 3 sides!
Equilateral Triangle     Definition:     An Equilateral triangle is triangle that has three     sides of equal length.    ...
Isosceles TriangleDefinition of Isosceles:Triangle that has two equal sides. Properties of Triangle:  Has 2 equal angles ...
Scalene Triangle   Definition of Scalene Triangle:   Scalene Triangle is triangle that has no   equal length.   Properties...
Right Triangle   Definition of right triangle:   Right triangle is triangle that has one   right angle.   Properties of Ri...
Obtuse Triangle    Definition of Obtuse Triangle is triangle    that has 1 obtuse angle > 90 degrees.    Properties of Obt...
Acute Triangle  Definition of acute triangle is triangle  that has 1 obtuse angle > 90 degrees.  Properties of Acute Trian...
Types of Acute TriangleEquilateral acute triangle   Isosceles acute triangle                                              ...
TRIANGLE           Phee.radhieanz@gmail.com
Phee.radhieanz@gmail.com
The ways                                         The Angles of Triangle1. Please sketch the triangle                      ...
The ways                                         The Angles of Triangle1. Please sketch the triangle                      ...
The ways                                           The Angles of Triangle1. Please sketch the triangle                    ...
The ways                                           The Angles of Triangle1. Please sketch the triangle                    ...
The ways                                           The Angels of Triangle1. Please sketch the triangle                    ...
The ways                                           The Angles of Triangle1. Please sketch the triangle                    ...
The ways                                           The Angles of Triangle1. Please sketch the triangle                    ...
The ways                                           The Angles of Triangle1. Please sketch the triangle                    ...
FIND THE ONE OF ANGLE OF TRIANGLE1.     60 ⁰                               Angle x = 30 ⁰                   x=?2.         ...
PERIMETER
DEFINITION   Perimeter is simply the distance around an object.
PERIMETER OF TRIANGLES   Finding the perimeter of a triangle is very easy. You    simply add up the three sides.         ...
EXAMPLE :   If a triangle has one side that is 22 cm long, another    that is 17 cm, and a third that is 30 cm long, what...
FIND THE PERIMETER OF TRIANGLE1.                    10 cm                                   Perimeter = 24 cm     6 cm    ...
THE AREA OF TRIANGLE
The Ways :                                                 The Area of Triangle1. Sketch a scalene trianglewith the   meas...
The ways                                               The Area of Triangle1. Please sketch the two congruent   triangle t...
FIND THE AREA OF TRIANGLE1.                       Area = 20 cm     5 cm            8 cm2.                       Area = 30 ...
FIND THE AREA OF TRIANGLE3.              15 cm                       Area = 48 cm     8 cm4.                       Area = ...
Phee.radhieanz@gmail.com
Phee.radhieanz@gmail.comISOSCELES TRIANGLE    Has at least two congruent                sides
Phee.radhieanz@gmail.comHOW TO SKETCH ISOSCELES TRIANGLE                                              C    1. Make a segme...
Phee.radhieanz@gmail.comEQUILATERAL TRIANGLE  Has three congruent sides
Phee.radhieanz@gmail.comHOW TO SKETCH EQUILATERAL TRIANGLE    1. Make a segment AB                                        ...
Phee.radhieanz@gmail.comRIGHT TRIANGLE       Has one right triangle
HOW TOsegment AB RIGHT TRIANGLE 1. Make a SKETCH2. Extend AB such that AB = AD3. Make a curve by initial point B          ...
DRAW PERPENDICULAR BISECTOR, BISECTOR,HEIGHT, AND MEDIAN OF TRIANGLE
DRAW PERPENDICULAR BISECTOR OFTRIANGLE                                        A 1. Draw any triangle 2. Mark every angle A...
PERPENDICULAR BISECTOR   A segment is called perpendicular bisector if and    only if the segment divide a side of triang...
DRAW BISECTOR OF TRIANGLE1. Draw any triangle                                              A2. Mark every angle A, B, and ...
BISECTOR   A segment is called bisector if and only if a segment    divide each angle of a triangle into two equal parts.
DRAW HEIGHT OF TRIANGLE1. Draw any triangle2. Mark every angle A, B, and C            A3. Draw the curve by initial point ...
HEIGHT   A segment is called height (altitude) in a triangle if    and only if the segment is perpendicular to a    trian...
DRAW MEDIAN OF TRIANGLE1. Draw any triangle                                          A2. Mark every angle A, B, and C3. Dr...
MEDIAN   A segment called median if and only if the segment    passing through one of the midpoint of a triangle    side ...
Triangle and quadrilateral
Triangle and quadrilateral
Upcoming SlideShare
Loading in …5
×

Triangle and quadrilateral

5,557 views

Published on

Triangle and quadrilateral

  1. 1. • Created By:• Yola Yaneta H.• Nurina Ayuningtyas• Wahyu Fajar S.• Yan Aditya P.
  2. 2. UADRILATERAL….?It is a geometrical shape havingexactly 4 sides. quad means fourand lateral means side .
  3. 3. IND THE QUADRILATERALS IN THE FOLLOWINGPICTURES…!
  4. 4.  A square is a quadrilateral where all sides are equal in length and all angles are equal.
  5. 5. QUARE it has four equal sides and four equal angles (90 degree angles, or right angles) The diagonals of a square bisect each other The diagonals of a square are perpendicular. Opposite sides of a square are both parallel and equal. The diagonals of a square are equal.
  6. 6. RECTANGLE Rectangle is a quadrilateral whose opposite sides in the same length and the angles are equal.
  7. 7. ECTANGLE• any quadrilateral with four right angles.• Opposite sides are parallel and congruent.• The diagonals bisect each other.• The diagonals are congruent.
  8. 8. PARALLELOGRAM A parallelogram is a quadrilateral in which the opposite sides are parallel.
  9. 9. ARALLELOGRAM Opposite sides are parallel and equal in length and opposite angles are equal (angles "a" are the same, and angles "b" are the same). The diagonal intersect each other and equal.
  10. 10. RHOMBUS
  11. 11. HOMBUS A four-sided shape where all sides have equal length. opposite sides are parallel opposite angles are equal. the diagonals of a rhombus bisect each other at right angles.
  12. 12. RAPEZOIDA trapezoid has one pair of opposite sidesparallel.
  13. 13. Isosceles trapezoid : if the sides that arent parallel are equal in lengthand both angles coming from a parallel side are equalRight trapezoid is a trapezoid having two right angles.
  14. 14. he Kite Kites are quadrilaterals with exactly two distinct pairs of adjacent are equal length.
  15. 15. he Kite The diagonals of a kite are perpendicular. Exactly one pair of opposite angles are congruent.
  16. 16.  How to find Perimeter??? A perimeter is a path that surrounds an area, so we just add all of the sides. A B 7 cm Perimeter ABCD= 4+4+7+7 = 22 cm 4 cm C D K L 3 cm Perimeter KLMN = 3+5+2+2 = 12 cm2 cm 2 cm M 5 cm N
  17. 17.  Perimeter square ABCD. AB= 3 cm  Perimeter ABCD= 3+3+3+3 = 12 cm Perimeter Rhombus ABCD. AB=4 cm  Perimeter ABCD= 4+4+4+4=16 cm Perimeter Parallelogram ABCD. AB=4 cm, BC=2 cm • PERIMETER ABCD= (4+2)2= 12 CM
  18. 18. DEFINE AREASQuadrilateral
  19. 19. SQUAREWhat is the area H=heightof this SQUARE?W=width
  20. 20. RECTANGLE7 14 21 28 35 42 496 13 20 27 34 41 485 12 19 26 33 40 47 What is the area H=height4 11 18 25 32 39 46 of this rectangle?3 10 17 24 31 38 452 9 16 23 30 37 441 8 15 22 29 36 43 W=width
  21. 21. RECTANGLE765 What is the area H=height4 of this rectangle?321 8 15 22 29 36 43 W=width
  22. 22. RECTANGLEWhat is the area H=heightof this rectangle?W=width
  23. 23. RECTANGLE7 14 21 28 35 42 49 56 636 13 20 27 34 41 48 55 625 12 19 26 33 40 47 54 61 What is the area H=height4 11 18 25 32 39 46 52 60 of this rectangle?3 10 17 24 31 38 45 52 592 9 16 23 30 37 44 51 581 8 15 22 29 36 43 50 57 W=width
  24. 24. RECTANGLE765 What is the area H=height4 of this rectangle?321 2 3 4 5 6 7 8 9 W=width
  25. 25. RECTANGLE765 What is the area H=height4 of this rectangle?321 2 3 4 5 6 7 8 9 W=width
  26. 26. RECTANGLE76 Arearectangle5 = What is the area Rows x Columns H=height4 = Widthrectangle? of this x Height321 2 3 4 5 6 7 8 9 W=width
  27. 27. PARALELOGRAM The length is m and the height is n Cut the height, and move it in the rights side. So we get rectangle now. The area is = m x n A B C D
  28. 28.  Given diagonal a=6cm and diagonal b=4cm. Draw into 2 rhombus.  Cut rhombus A into 4 equal parts.RHOMBUS  Paste it into rhombus B, so we get new rectangle.  The area of 2 rhombus = a X b  So, the area of 1 rhombus = ½ (a X b) (A) (B) Diagonal “a” 6 cm Diagonal “b” 4 cm
  29. 29.  Given diagonal a=9cm and diagonal b=4cm. Draw into 2 kites.  Cut kites A into 4 equal parts.KITES  Paste it into kites B, so we get new rectangle.  The area of 2 kites = a X b  So, the area of 1 kites = ½ (a X b) Diagonal “b” 4 cm (A) (B) Diagonal “a” 9 cm
  30. 30. TRAPEZOID Trapezoid with upper=a, base=b, height=h Make it again with same trapezoid and flip it. Cut the triangle, and paste it to right side. So we get rectagle now. Area of rectagle = 2 trapezoid= (a+b)xh Area of trapezoid = ( a b) h 2 a b h b a
  31. 31. TRIANGLE Phee.radhieanz@gmail.com
  32. 32. TrianglesShapes with 3 sides!
  33. 33. Equilateral Triangle Definition: An Equilateral triangle is triangle that has three sides of equal length. Properties of an equilateral triangle:  Has 3 equal angles  Each angle is a 60o angle  Has 3 lines of symmetry
  34. 34. Isosceles TriangleDefinition of Isosceles:Triangle that has two equal sides. Properties of Triangle:  Has 2 equal angles  Has 1 line of symmetry
  35. 35. Scalene Triangle Definition of Scalene Triangle: Scalene Triangle is triangle that has no equal length. Properties of Scalene Triangle:  Has NO equal angles Has NO lines of symmetry  Is an irregular shape
  36. 36. Right Triangle Definition of right triangle: Right triangle is triangle that has one right angle. Properties of Right Triangle:  Has 1 right angle  May be an isosceles triangle May have 1 line of symmetry It will be isosceles and have 1 line of symmetry when these 2 sides are equal.
  37. 37. Obtuse Triangle Definition of Obtuse Triangle is triangle that has 1 obtuse angle > 90 degrees. Properties of Obtuse Triangle:  Has 2 acute angle. May have 1 line of symmetry.
  38. 38. Acute Triangle Definition of acute triangle is triangle that has 1 obtuse angle > 90 degrees. Properties of Acute Triangle:  Has 2 acute angle. May have 1 line of symmetry.
  39. 39. Types of Acute TriangleEquilateral acute triangle Isosceles acute triangle Scalene acute triangle
  40. 40. TRIANGLE Phee.radhieanz@gmail.com
  41. 41. Phee.radhieanz@gmail.com
  42. 42. The ways The Angles of Triangle1. Please sketch the triangle c2. Cut based on sides! a b3. Fine the angles of triangle!4. Give name to each of angles5. Cut the corner of the each angle of triangle Phee.radhieanz@gmail.com
  43. 43. The ways The Angles of Triangle1. Please sketch the triangle c2. Cut based on sides! a b3. Fine the angles of triangle!4. Give name to each of angles5. Cut the corner of the each angle of triangle Phee.radhieanz@gmail.com
  44. 44. The ways The Angles of Triangle1. Please sketch the triangle c2. Cut based on sides! a b3. Fine the angles of triangle!4. Give name to each of angles5. Cut the corner of the each angle of triangle6. Arrange them so become straight angle Phee.radhieanz@gmail.com
  45. 45. The ways The Angles of Triangle1. Please sketch the triangle c2. Cut based on sides! a b3. Fine the angles of triangle!4. Give name to each of angles5. Cut the corner of the each angle of triangle6. Arrange them so become straight angle Phee.radhieanz@gmail.com
  46. 46. The ways The Angels of Triangle1. Please sketch the triangle c2. Cut based on sides! a b3. Fine the angles of triangle!4. Give name to each of angles5. Cut the corner of the each angle of triangle6. Arrange them so become straight angle Phee.radhieanz@gmail.com
  47. 47. The ways The Angles of Triangle1. Please sketch the triangle b c2. Cut based on sides! a3. Fine the angles of triangle!4. Give name to each of angles5. Cut the corner of the each angle of triangle6. Arrange them so become straight angle Phee.radhieanz@gmail.com
  48. 48. The ways The Angles of Triangle1. Please sketch the triangle b c2. Cut based on sides! a3. Fine the angles of triangle!4. Give name to each of angles5. Cut the corner of the each angle of triangle6. Arrange them so become straight angle Phee.radhieanz@gmail.com
  49. 49. The ways The Angles of Triangle1. Please sketch the triangle b c2. Cut based on sides! a3. Fine the angles of triangle! 180 degrees4. Give name to each of angles Conclution5. Cut the corner of the each angle of triangle The sum of the angles of a6. Arrange them so become straight angle triangle is 180° a + b + c = 180° Phee.radhieanz@gmail.com
  50. 50. FIND THE ONE OF ANGLE OF TRIANGLE1. 60 ⁰ Angle x = 30 ⁰ x=?2. Angle x = 50 ⁰ 60 ⁰ 70 ⁰ x=?
  51. 51. PERIMETER
  52. 52. DEFINITION Perimeter is simply the distance around an object.
  53. 53. PERIMETER OF TRIANGLES Finding the perimeter of a triangle is very easy. You simply add up the three sides. a b c Perimeter = a + b + c
  54. 54. EXAMPLE : If a triangle has one side that is 22 cm long, another that is 17 cm, and a third that is 30 cm long, what is the perimeter? 22cm 17cm 30cmPerimeter = 22cm + 17cm + 30cm = 69cm
  55. 55. FIND THE PERIMETER OF TRIANGLE1. 10 cm Perimeter = 24 cm 6 cm 8 cm2. Perimeter = 28 m 6m 12 m 10 m
  56. 56. THE AREA OF TRIANGLE
  57. 57. The Ways : The Area of Triangle1. Sketch a scalene trianglewith the measurement scalene leg and height to the block paper h2. Cut according to sides !3. Define the leg and the height of triangle!4. Cut the triangle with ½ of height. w What the planes that can be formed?5. Cut the small triangle crossing the Conclution height line! What the planes that can be formed?6. Arrange there planes so become Because the area of rectangle, rectangle! A = w × h, the area of triangle,7. The area of triangle, A=w×½h =8. Wide of rectangle = ½ h triangle width of the rectangle = leg of triangle
  58. 58. The ways The Area of Triangle1. Please sketch the two congruent triangle to the block paper!2. Cut based on sides! h w3. Define the leg and height of triangle!4. Arrange this triangles so become Conclution rectangle! Suppose the area of rectangle, A=w h, so the area of 2 triangle,5. Corrolary 2 triangles forming the A = w h, so we ca get the formula of rectangle so: triangle ? w leg = …. rectangle, and A = 1 (w h) height =h …. rectangle ? 2
  59. 59. FIND THE AREA OF TRIANGLE1. Area = 20 cm 5 cm 8 cm2. Area = 30 m 6m 10 m
  60. 60. FIND THE AREA OF TRIANGLE3. 15 cm Area = 48 cm 8 cm4. Area = 80 m 8m 20 m
  61. 61. Phee.radhieanz@gmail.com
  62. 62. Phee.radhieanz@gmail.comISOSCELES TRIANGLE Has at least two congruent sides
  63. 63. Phee.radhieanz@gmail.comHOW TO SKETCH ISOSCELES TRIANGLE C 1. Make a segment AB 2. Make a curve by scalene radius from initial point A 3. Make a curve by scalene radius from initial point B 4. Please mark the intersect of two curve by point C 5. Connect all of there points. A B
  64. 64. Phee.radhieanz@gmail.comEQUILATERAL TRIANGLE Has three congruent sides
  65. 65. Phee.radhieanz@gmail.comHOW TO SKETCH EQUILATERAL TRIANGLE 1. Make a segment AB C 2. Make a curve by radius from initial point B until point A 3. Make a curve by radius from initial point A until point B 4. Please mark the intersect of two curve by point C 5. Connect all of there points. B A
  66. 66. Phee.radhieanz@gmail.comRIGHT TRIANGLE Has one right triangle
  67. 67. HOW TOsegment AB RIGHT TRIANGLE 1. Make a SKETCH2. Extend AB such that AB = AD3. Make a curve by initial point B C4. Make a curve by initial point D5. Take a line from A through intersection point6. Label the edge of the segment by C7. Connect C and B D B A
  68. 68. DRAW PERPENDICULAR BISECTOR, BISECTOR,HEIGHT, AND MEDIAN OF TRIANGLE
  69. 69. DRAW PERPENDICULAR BISECTOR OFTRIANGLE A 1. Draw any triangle 2. Mark every angle A, B, and C 3. Draw the curve by initial point at B 4. Draw the curve by initial point at C C 5. Draw the segment at B intersection of curve
  70. 70. PERPENDICULAR BISECTOR A segment is called perpendicular bisector if and only if the segment divide a side of triangle into two congruent sides and perpendicular.
  71. 71. DRAW BISECTOR OF TRIANGLE1. Draw any triangle A2. Mark every angle A, B, and C3. Draw the curve by initial point at A4. Give name there intersection D E point D and E5. Draw the curve by initial point at D6. Draw the curve by initial point B C at E7. Give name O in this intersection O of two curves8. Connect AO
  72. 72. BISECTOR A segment is called bisector if and only if a segment divide each angle of a triangle into two equal parts.
  73. 73. DRAW HEIGHT OF TRIANGLE1. Draw any triangle2. Mark every angle A, B, and C A3. Draw the curve by initial point A , and by the radius until intersect line BC4. Give name there intersection point D and E5. Sketch the curve by the initial point D6. Sketch the curve by the initial point E B C E D7. Sketch a segment from A to intersection of two curves
  74. 74. HEIGHT A segment is called height (altitude) in a triangle if and only if the segment is perpendicular to a triangle side and passing through the vertex in front of the side.
  75. 75. DRAW MEDIAN OF TRIANGLE1. Draw any triangle A2. Mark every angle A, B, and C3. Draw the curve by initial point at B4. Draw the curve by initial point at C5. Draw the segment at intersection of curve and call it segment k B C O6. Give name the intersection of BC and k by point O7. Connect AO by the line k
  76. 76. MEDIAN A segment called median if and only if the segment passing through one of the midpoint of a triangle side and the vertex in front of the side.

×