1. • Created By:
• Yola Yaneta H.
• Nurina Ayuningtyas
• Wahyu Fajar S.
• Yan Aditya P.

2. UADRILATERAL….?
It is a geometrical shape having
exactly 4 sides. quad means four
and lateral means side .

3. IND THE QUADRILATERALS IN THE FOLLOWING
PICTURES…!

4.  A square is a quadrilateral where all sides
are equal in length and all angles are equal.

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. RECTANGLE
 Rectangle is a quadrilateral whose opposite sides
in the same length and the angles are equal.

7. ECTANGLE
• any quadrilateral with four right angles.
• Opposite sides are parallel and congruent.
• The diagonals bisect each other.
• The diagonals are congruent.

8. PARALLELOGRAM
A parallelogram is a quadrilateral in which the opposite
sides are parallel.

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. RHOMBUS

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. RAPEZOID
A trapezoid has one pair of opposite sides
parallel.

13. Isosceles trapezoid : if the sides that aren't parallel are equal in length
and both angles coming from a parallel side are equal
Right trapezoid is a trapezoid having two right angles.

14. he Kite
Kites are quadrilaterals with exactly two distinct pairs
of adjacent are equal length.

15. he Kite
 The diagonals of a kite are perpendicular.
 Exactly one pair of opposite angles are congruent.

17.  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 cm
2 cm 2 cm
M 5 cm N

18.  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

19. DEFINE AREAS
Quadrilateral

20. SQUARE
What is the area H=height
of this SQUARE?
W=width

21. RECTANGLE
7 14 21 28 35 42 49
6 13 20 27 34 41 48
5 12 19 26 33 40 47
What is the area H=height
4 11 18 25 32 39 46
of this rectangle?
3 10 17 24 31 38 45
2 9 16 23 30 37 44
1 8 15 22 29 36 43
W=width

22. RECTANGLE
7
6
5
What is the area H=height
4
of this rectangle?
3
2
1 8 15 22 29 36 43
W=width

23. RECTANGLE
What is the area H=height
of this rectangle?
W=width

24. RECTANGLE
7 14 21 28 35 42 49 56 63
6 13 20 27 34 41 48 55 62
5 12 19 26 33 40 47 54 61
What is the area H=height
4 11 18 25 32 39 46 52 60
of this rectangle?
3 10 17 24 31 38 45 52 59
2 9 16 23 30 37 44 51 58
1 8 15 22 29 36 43 50 57
W=width

25. RECTANGLE
7
6
5
What is the area H=height
4
of this rectangle?
3
2
1 2 3 4 5 6 7 8 9
W=width

26. RECTANGLE
7
6
5
What is the area H=height
4
of this rectangle?
3
2
1 2 3 4 5 6 7 8 9
W=width

27. RECTANGLE
7
6
Arearectangle
5
= What is the area
Rows x Columns H=height
4
= Widthrectangle?
of this x Height
3
2
1 2 3 4 5 6 7 8 9
W=width

28. 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

29.  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

30.  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

31. 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

32. TRIANGLE
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33. Triangles
Shapes with 3 sides!

34. 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

35. Isosceles Triangle
Definition of Isosceles:
Triangle that has two equal sides.
Properties of Triangle:
 Has 2 equal angles
 Has 1 line of symmetry

36. 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

37. 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.

38. 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.

39. 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.

40. Types of Acute Triangle
Equilateral acute triangle Isosceles acute triangle
Scalene acute triangle

41. TRIANGLE
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43. The ways
The Angles of Triangle
1. Please sketch the triangle
c
2. Cut based on sides!
a
b
3. Fine the angles of triangle!
4. Give name to each of angles
5. Cut the corner of the each angle of
triangle
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44. The ways
The Angles of Triangle
1. Please sketch the triangle
c
2. Cut based on sides!
a
b
3. Fine the angles of triangle!
4. Give name to each of angles
5. Cut the corner of the each angle of
triangle
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45. The ways
The Angles of Triangle
1. Please sketch the triangle
c
2. Cut based on sides!
a
b
3. Fine the angles of triangle!
4. Give name to each of angles
5. Cut the corner of the each angle of
triangle
6. Arrange them so become straight angle
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46. The ways
The Angles of Triangle
1. Please sketch the triangle
c
2. Cut based on sides!
a
b
3. Fine the angles of triangle!
4. Give name to each of angles
5. Cut the corner of the each angle of
triangle
6. Arrange them so become straight angle
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47. The ways
The Angels of Triangle
1. Please sketch the triangle
c
2. Cut based on sides!
a
b
3. Fine the angles of triangle!
4. Give name to each of angles
5. Cut the corner of the each angle of
triangle
6. Arrange them so become straight angle
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48. The ways
The Angles of Triangle
1. Please sketch the triangle
b
c
2. Cut based on sides!
a
3. Fine the angles of triangle!
4. Give name to each of angles
5. Cut the corner of the each angle of
triangle
6. Arrange them so become straight angle
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49. The ways
The Angles of Triangle
1. Please sketch the triangle
b
c
2. Cut based on sides! a
3. Fine the angles of triangle!
4. Give name to each of angles
5. Cut the corner of the each angle of
triangle
6. Arrange them so become straight angle
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50. The ways
The Angles of Triangle
1. Please sketch the triangle
b
c
2. Cut based on sides! a
3. Fine the angles of triangle! 180 degrees
4. Give name to each of angles
Conclution
5. Cut the corner of the each angle of
triangle
The sum of the angles of a
6. Arrange them so become straight angle
triangle is 180°
a + b + c = 180°
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51. FIND THE ONE OF ANGLE OF TRIANGLE
1.
60 ⁰
Angle x = 30 ⁰
x=?
2.
Angle x = 50 ⁰
60 ⁰
70 ⁰ x=?

52. PERIMETER

53. DEFINITION
 Perimeter is simply the distance around an object.

54. 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

55. 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
30cm
Perimeter = 22cm + 17cm + 30cm = 69cm

56. FIND THE PERIMETER OF TRIANGLE
1.
10 cm
Perimeter = 24 cm
6 cm
8 cm
2.
Perimeter = 28 m
6m 12 m
10 m

57. THE AREA OF TRIANGLE

58. The Ways :
The Area of Triangle
1. Sketch a scalene trianglewith the
measurement scalene leg and height
to the block paper
h
2. 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

59. The ways
The Area of Triangle
1. Please sketch the two congruent
triangle to the block paper!
2. Cut based on sides! h
w
3. 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

60. FIND THE AREA OF TRIANGLE
1.
Area = 20 cm
5 cm
8 cm
2.
Area = 30 m
6m
10 m

61. FIND THE AREA OF TRIANGLE
3.
15 cm
Area = 48 cm
8 cm
4.
Area = 80 m
8m
20 m

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ISOSCELES TRIANGLE
Has at least two congruent
sides

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HOW 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

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EQUILATERAL TRIANGLE
Has three congruent sides

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HOW 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

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RIGHT TRIANGLE
Has one right triangle

68. HOW TOsegment AB RIGHT TRIANGLE
1. Make a SKETCH
2. Extend AB such that AB = AD
3. Make a curve by initial point B
C
4. Make a curve by initial point D
5. Take a line from A through
intersection point
6. Label the edge of the segment by
C
7. Connect C and B
D B
A

69. DRAW PERPENDICULAR BISECTOR, BISECTOR,
HEIGHT, AND MEDIAN OF TRIANGLE

70. DRAW PERPENDICULAR BISECTOR OF
TRIANGLE
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

71. 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.

72. DRAW BISECTOR OF TRIANGLE
1. Draw any triangle
A
2. Mark every angle A, B, and C
3. Draw the curve by initial point
at A
4. Give name there intersection D
E
point D and E
5. Draw the curve by initial point
at D
6. Draw the curve by initial point B C
at E
7. Give name O in this intersection O
of two curves
8. Connect AO

73. BISECTOR
 A segment is called bisector if and only if a segment
divide each angle of a triangle into two equal parts.

74. DRAW HEIGHT OF TRIANGLE
1. Draw any triangle
2. Mark every angle A, B, and C A
3. Draw the curve by initial point
A , and by the radius until
intersect line BC
4. Give name there intersection
point D and E
5. Sketch the curve by the initial
point D
6. Sketch the curve by the initial
point E B C
E D
7. Sketch a segment from A to
intersection of two curves

75. 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.

76. DRAW MEDIAN OF TRIANGLE
1. Draw any triangle
A
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
5. Draw the segment at intersection
of curve and call it segment k
B C
O
6. Give name the intersection of BC
and k by point O
7. Connect AO by the line k

77. 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.