Triangle and quadrilateral
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Quadrilateral and Triangle • Created By: • Yola Yaneta H. • Nurina Ayuningtyas • Wahyu Fajar S. • Yan Aditya P.
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Transcript of Triangle and quadrilateral
Quadrilateral and Triangle
• Created By:• Yola Yaneta H.• Nurina Ayuningtyas• Wahyu Fajar S.• Yan Aditya P.
UADRILATERAL….?
It is a geometrical shape having exactly 4 sides. quad means fourand lateral means side .
IND THE QUADRILATERALS IN THE FOLLOWING PICTURES…!
A square is a quadrilateral where all sides are equal in length and all angles are equal.
Definition of quare
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.
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 other.• The diagonals are congruent.
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, and angles "b" are the same). The diagonal intersect each other and equal.
RHOMBUS
A RHOMBUS IS a parallelogram all four sides are equal in length.
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.
RAPEZOID
A trapezoid has one pair of opposite sides parallel.
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.
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.
he Kite
Quadrilateral
Kite
Trapezoid
Isosceles Trapezoid
Parallelogram
Rectangle
Square
Rhombus
How to find Perimeter???
A perimeter is a path that surrounds an area, so we just add all of the sides.
A B
C D
7 cm
4 cm
Perimeter ABCD= 4+4+7+7 = 22 cm
K L
M N
3 cm
5 cm
2 cm2 cmPerimeter KLMN = 3+5+2+2 = 12 cm
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
DEFINE AREASQuadrilateral
SQUARE
What is the area of this SQUARE?
W=width
H=height
RECTANGLE
W=width
H=height What is the area of this rectangle?
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RECTANGLE
W=width
H=height What is the area of this rectangle?
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Area of Rectangle:Width x height
RECTANGLE
W=width
H=height What is the area of this rectangle?
RECTANGLE
W=width
H=height What is the area of this rectangle?
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RECTANGLE
W=width
H=height What is the area of this rectangle?
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RECTANGLE
W=width
H=height What is the area of this rectangle?
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RECTANGLE
W=width
H=height What is the area of this rectangle?
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Arearectangle
= Rows x Columns
= Width x Height
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
DC
n
m
RHOMBUS
Given diagonal a=6cm and diagonal b=4cm. Draw into 2 rhombus.
Cut rhombus A into 4 equal parts. 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
KITES
Given diagonal a=9cm and diagonal b=4cm. Draw into 2 kites.
Cut kites A into 4 equal parts. 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)
(A)
(B)
Diagonal “a” 9 cm
Diagonal “b” 4 cm
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 a
b
h
2
)( hba
Triangles
Shapes with 3 sides!
Equilateral Triangle
Properties of an equilateral triangle:
Has 3 equal angles
Each angle is a 60o angle
Has 3 lines of symmetry
Definition:
An Equilateral triangle is triangle that has three sides of equal length.
Isosceles Triangle
Properties of Triangle:
Has 2 equal angles
Has 1 line of symmetry
Definition of Isosceles:
Triangle that has two equal sides.
Scalene Triangle
Properties of Scalene Triangle:
Has NO equal angles
Has NO lines of symmetry
Is an irregular shape
Definition of Scalene Triangle:
Scalene Triangle is triangle that has no equal length.
Right Triangle
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.
Definition of right triangle:
Right triangle is triangle that has one right angle.
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.
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.
Types of Acute Triangle
Equilateral acute triangle Isosceles acute triangleScalene acute triangle
The ways
1. Please sketch the triangle
The Angles of Triangle
2. Cut based on sides!
3. Fine the angles of triangle!
5. Cut the corner of the each angle of triangle
4. Give name to each of angles
ab
c
The ways
1. Please sketch the triangle
5. Cut the corner of the each angle of triangle
The Angles of Triangle
2. Cut based on sides!
3. Fine the angles of triangle!
ab
c
4. Give name to each of angles
The ways
1. Please sketch the triangle
5. Cut the corner of the each angle of triangle
The Angles of Triangle
2. Cut based on sides!
3. Fine the angles of triangle!
6. Arrange them so become straight angle
ab
c
4. Give name to each of angles
The ways
1. Please sketch the triangle
5. Cut the corner of the each angle of triangle
The Angles of Triangle
2. Cut based on sides!
3. Fine the angles of triangle!
6. Arrange them so become straight angle
ab
c
4. Give name to each of angles
The ways
1. Please sketch the triangle
5. Cut the corner of the each angle of triangle
The Angels of Triangle
2. Cut based on sides!
3. Fine the angles of triangle!
6. Arrange them so become straight angle
ab
c
4. Give name to each of angles
The ways
1. Please sketch the triangle
5. Cut the corner of the each angle of triangle
The Angles of Triangle
2. Cut based on sides!
3. Fine the angles of triangle!
6. Arrange them so become straight angle
a
bc
4. Give name to each of angles
The ways
1. Please sketch the triangle
5. Cut the corner of the each angle of triangle
The Angles of Triangle
2. Cut based on sides!
3. Fine the angles of triangle!
6. Arrange them so become straight angle
a
bc
4. Give name to each of angles
The ways
1. Please sketch the triangle
5. Cut the corner of the each angle of triangle
The Angles of Triangle
2. Cut based on sides!
3. Fine the angles of triangle!
Conclution
6. Arrange them so become straight angleThe sum of the angles of
a triangle is 180°
a + b + c = 180°
180 degrees
a
bc
4. Give name to each of angles
FIND THE ONE OF ANGLE OF TRIANGLE
1.
2.
Angle x = 30 ⁰
Angle x = 50 ⁰
60 ⁰
x=?
60 ⁰
70 ⁰ x=?
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.
c
a b
Perimeter = a + b + c
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?
Perimeter = 22cm + 17cm + 30cm = 69cm
30cm
22cm
17cm
FIND THE PERIMETER OF TRIANGLE
1.
2.
6 cm
8 cm
6 m
10 m
Perimeter = 24 cm
Perimeter = 28 m
10 cm
12 m
THE AREA OF TRIANGLE
The Ways :
1. Sketch a scalene trianglewith the measurement scalene leg and height to the block paper
4. Cut the triangle with ½ of height. What the planes that can be formed?
2. Cut according to sides !
3. Define the leg and the height of triangle!
7. The area of triangle,
=
5. Cut the small triangle crossing the height line! What the planes that can be formed?
The Area of Triangle
w
Conclution
Because the area of rectangle,
A = w × h, the area of triangle,
A = w × ½ h
6. Arrange there planes so become rectangle!
h
8. Wide of rectangle = ½ h triangle
width of the rectangle = leg of triangle
The ways
1. Please sketch the two congruent triangle to the block paper!
4. Arrange this triangles so become rectangle!
The Area of Triangle
2. Cut based on sides!
3. Define the leg and height of triangle!
w
h
5. Corrolary 2 triangles forming the rectangle so:
leg = …. rectangle, and
height = …. rectangle
w
h?
?
Suppose the area of rectangle,
A = w h, so the area of 2 triangle,
A = w h, so we ca get the formula of triangle
A = (w h)2
1
Conclution
FIND THE AREA OF TRIANGLE
1.
2.
5 cm
8 cm
6 m
10 m
Area = 20 cm
Area = 30 m
FIND THE AREA OF TRIANGLE
3.
4.
8 cm
15 cm
8 m
20 m
Area = 48 cm
Area = 80 m
HOW TO SKETCH ISOSCELES TRIANGLE
A B
C1. 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 B4. Please mark the intersect of two curve by point C5. Connect all of there points.
HOW TO SKETCH EQUILATERAL TRIANGLE
AB
C1. Make a segment AB
2. Make a curve by radius from initial point B until point A3. Make a curve by radius from initial point A until point B4. Please mark the intersect of two curve by point C5. Connect all of there points.
HOW TO SKETCH RIGHT TRIANGLE
AB
C
D
1. Make a segment AB2. Extend AB such that AB = AD3. Make a curve by initial point B4. 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
DRAW PERPENDICULAR BISECTOR OF TRIANGLE
A
B C
1. Draw any triangle
2. 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
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.
DRAW BISECTOR OF TRIANGLE
A
B C
1. Draw any triangle
2. Mark every angle A, B, and C3. Draw the curve by initial point at A
5. Draw the curve by initial point at D
4. Give name there intersection point D and E
DE
6. Draw the curve by initial point at E7. Give name O in this intersection of two curves
O
8. Connect AO
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 TRIANGLE
A
B C
1. Draw any triangle
2. Mark every angle A, B, and C3. Draw the curve by initial point A , and by the radius until intersect line BC4. Give name there intersection point D and E
DE
5. Sketch the curve by the initial point D6. Sketch the curve by the initial point E7. Sketch a segment from A to intersection of two curves
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.
DRAW MEDIAN OF TRIANGLE
A
B C
1. Draw any triangle
2. 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 k6. Give name the intersection of BC and k by point O
k7. Connect AO by the line
O
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.
THANK YOUMERCYDUNKE
MUCUS GRACIASARIGATOXIE-XIE
TERIMA KASIH
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