Introduction to Geometry

1
IntroductiontoGeometry
2
Figures that lie in a plane are called plane
figures.
3
Figures that lie in a plane are called plane
figures.

• These are all plane figures.

4
A polygon is a plane closed figure determined by
three or more line segments.
5
A polygon is a plane closed figure determined by
three or more line segments.

• Triangle 3 sides

6
A polygon is a plane closed figure determined by
three or more line segments.

• Triangle 3 sides
• Quadrilateral 4 sides

7
A polygon is a plane closed figure determined by
three or more line segments.

• Triangle 3 sides
• Quadrilateral 4 sides
• Pentagon 5 sides

8
A polygon is a plane closed figure determined by
three or more line segments.

• Triangle 3 sides
• Quadrilateral 4 sides
• Pentagon 5 sides
• Hexagon 6 sides

9
A polygon is a plane closed figure determined by
three or more line segments.

• Triangle 3 sides
• Quadrilateral 4 sides
• Pentagon 5 sides
• Hexagon 6 sides
• Heptagon 7 sides

10
A polygon is a plane closed figure determined by
three or more line segments.

• Triangle 3 sides
• Quadrilateral 4 sides
• Pentagon 5 sides
• Hexagon 6 sides
• Heptagon 7 sides
• Octagon 8 sides

11
A polygon is a plane closed figure determined by
three or more line segments.

• Triangle 3 sides
• Quadrilateral 4 sides
• Pentagon 5 sides
• Hexagon 6 sides
• Heptagon 7 sides
• Octagon 8 sides
• Nonagon 9 sides

12
A polygon is a plane closed figure determined by
three or more line segments.

• Triangle 3 sides
• Quadrilateral 4 sides
• Pentagon 5 sides
• Hexagon 6 sides
• Heptagon 7 sides
• Octagon 8 sides
• Nonagon 9 sides
• Decagon 10 sides

13
(No Transcript)
14
What happens as the number of sides of a polygon
increases?
15
As the number of sides increased, the plane
figure became more circular.

• A circle is defined as a set of points in a plane
  equidistant from a given point called the center.

16
(No Transcript)
17
A diameter is equal to two radii.
d 2r
18
A triangle may be classified byeither its sides
or its angles.
19
Classification by SIDES
20
Classification by SIDES

21
Classification by SIDES

• Equilateral

22
Classification by SIDES

• Equilateral

23
Classification by SIDES

• Equilateral
• Isosceles

24
Classification by SIDES

• Equilateral
• Isosceles

25
Classification by SIDES

• Equilateral
• Isosceles
• Scalene

26
Classification by ANGLES

27
Classification by ANGLES

28
Classification by ANGLES

• Acute

29
Classification by ANGLES

• Acute

30
Classification by ANGLES

• Acute
• Obtuse

31
Classification by ANGLES

• Acute
• Obtuse

32
Classification by ANGLES

• Acute
• Obtuse
• Right

33
What is the sum of the measures of the interior
angles of a triangle?
34
B
A
C
The sum of the measures of the interior angles of
a triangle is 180 degrees.
35
A quadrilateral may be classified by either
1. its sides or 2. its sides and its angles.
36
Some quadrilaterals are

• parallelograms

37
Quadrilateral
Parallelogram
38
Some quadrilaterals are

• parallelograms
• or

• trapezoids.

39
Quadrilateral
Trapezoid
Parallelogram
40
If the two nonparallel sides of a trapezoid are
equal in length,it is called anisosceles
trapezoid.
41
Quadrilateral
Trapezoid
Parallelogram
Isosceles Trapezoid
42
If all the angles of a parallelogram measure 90
,it is called arectangle.
43
Quadrilateral
Trapezoid
Parallelogram
Rectangle
Isosceles Trapezoid
44
If all the sides of a parallelogram are the same
length,it is called arhombus.
45
Quadrilateral
Trapezoid
Parallelogram
Rectangle
Isosceles Trapezoid
Rhombus
46
If all the sides of a parallelogram are the same
length and the angles measure 90 ,it is called
asquare.
47
Quadrilateral
Trapezoid
Parallelogram
Rectangle
Isosceles Trapezoid
Rhombus
48
Two measures of plane figures are important to
mathematicians

• a. the distance around a plane figure
• called the perimeter or circumference
• and
• b. the number of square units in the interior
  of a plane figure
  
• called the area.

49
Perimeter
The perimeter of every polygon may be found by
adding all the sides.
50
Equilateral Triangle Shortcut
51
Rectangle Shortcut
52
Perimeter Shortcuts

• Regular Polygons (all sides equal)
• Equilateral Triangle P 3s
• Square (and Rhombus) P 4s
• Regular Pentagon P 5s
• and so forth
• Rectangle (opposite sides equal) P 2l 2w

53
The circumference is the distance around a circle.
54
The circumference is the distance around a circle.
orC ? d
Since d2r, C ? (2r)
orC 2?r.
55
P a b c
P a b c d
P 2l 2w
P 4s
P 4s
P a b c d
C ?d or 2?r
56
Area
Area is measured in square units. A square unit
is a square one unit on each side.
For example, start with a rectangle with length
(l) 3 units and width (w) 2 units.
A 6 units2 A 3 . 2 units2 A l . w
57
The diagonal of a parallelogram forms 2
congruent triangles.
3 X 2 6
bh A
58
The area of a circle is a little more than 3
squares, r x r.
A ? (r x r)
A ? r2
59
Given a Circle of radius, r .
60
(No Transcript)
61
Notice the rectangular shape.
A lw
A (?r)r
A ?r2
62
P a b c
A bh
P a b c d
P 2l 2w
A lw
P 4s
A bh
A s2
P 4s
P a b c d
C ?d or 2?r
A ?r2
63
(No Transcript)