Geometry - PowerPoint PPT Presentation

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Geometry

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Geometry – PowerPoint PPT presentation

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Title: Geometry


1
Geometry
POINT
A point is an exact location in space. A point
has no length or width. To identify a point you
use a dot and name it with a capital letter.
For example point A would look like this -
A
.
You would say this is Point A.
2
Geometry
Line
A line is a straight path of points that never
ends. It goes on forever in two directions.
When you draw a line you name it by using any two
letters on the line. Another way to name a line
is to use a single small letter.
.
.
A
B
a
3
Geometry
.
.
A
B
a
4
Geometry
Types of lines
A horizontal line goes straight across like the
horizon.
HORIZONTAL LINES
.
.
5
Geometry
More lines
Intersecting lines
Intersecting lines are lines that cross. They
cross at a point. For example, think about
streets that meet and cross at intersections.
Line AB intersects line CD at point E.
6
Geometry
More lines
PERPENDICULAR LINES
When two intersecting lines meet to form square
corners, they are called perpendicular lines.
7
Geometry
More lines
PARALLEL LINES
Parallel lines are always the same distance
apart. They will never cross, or intersect, one
another, like railroad tracks.
8
Geometry
Think of a line as a rope that never ends. You
can cut the rope into pieces. Each piece is a
segment of a the rope.
LINE SEGMENT
A line segment is a part of a line.
You name a line segment by using its two
endpoints.
9
Geometry
RAY
A ray is a part of a line. It has one endpoint
and goes on forever in one direction.
Use the endpoint as the first letter when
writing the name of a ray.
endpoint
When you see a little One-headed arrow,
say ray.
Ray OB
10
Geometry
ANGLE
An angle is formed when two rays meet at an
endpoint.
The endpoint is called the vertex of the angle.
Point B is the vertex of the angle.
11
Geometry
You can name an angle by writing the point on one
ray, the vertex, and the point on the other ray.
When you see a sharp corner symbol say angle.
The vertex is always written in the middle.
12
Geometry
KINDS OF ANGLES
You can name angles by how the measure compared
to 90 degrees.
ACUTE ANGLES
Acute angles measure less than 90 degrees.
13
Geometry
KINDS OF ANGLES
You can name angles by how the measure compared
to 90 degrees.
OBTUSE ANGLES
Obtuse angles measure greater than 90 degrees.
14
Geometry
KINDS OF ANGLES
You can name angles by how the measure compared
to 90 degrees.
RIGHT ANGLES
Right angles measure exactly 90 degrees.
15
Geometry
KINDS OF ANGLES
A straight angle measures 180 degrees. It looks
like a straight line.
STRAIGHT ANGLES
16
Geometry
Polygons
A polygon is a closed figure whose sides are all
line segments.
Not Polygons
Polygons
17
Geometry
Polygons
The name of a polygon depends on the number of
sides it has.
triangle 3 sides
quadrilateral 4 sides
pentagon 5 sides
hexagon 6 sides
octagon 8 sides
18
Geometry
Polygons
The name of a polygon depends on the number of
sides it has.
A polygon that has all sides the same length and
all angles the same measure is called a regular
polygon.
19
Geometry
Quadrilaterals
A quadrilateral has 4 sides.
Some quadrilaterals have more than one name.
This quadrilateral is also called a trapezoid.
A trapezoid has exactly one pair of parallel
lines.
20
Geometry
Quadrilaterals
A quadrilateral has 4 sides.
These quadrilaterals are also called
parallelograms.
A parallelogram has two pairs of sides that are
the same length and are parallel.
The sides marked in red are parallel to each
other. They are the same length. The sides
marked in green are parallel to each other. They
are the same length.
21
Geometry
Lets look at just the parallelograms!
Each of these two parallelograms is also called a
rhombus.
A rhombus has all sides the same length.
22
Geometry
Lets continue to just look at the parallelograms.
Each of these two parallelograms is also called a
rectangle.
A rectangle has 4 right angles.
23
Geometry
This figure is both a rhombus and a rectangle.
It has all sides the same length and it has 4
right angles.
It is called a square.
24
Geometry
A triangle is a polygon with three sides.
Triangles can be named two different ways.
First
Named by its angles.
25
Geometry
Triangles can be named two different ways.
Second
Named by the length of its sides.
26
Geometry
Solid Figures
Solid figures have three dimensions length,
width, and height.
Simple solid figure
CONES
SPHERES
CYLINDERS
PRISMS
PYRAMIDS
27
Geometry
Names of Solid Figures
prisms
A 3-dimensional figure that has two congruent and
parallel faces that are polygons. The rest of
the faces are parallelograms.
28
Geometry
Names of Solid Figures
pyramids
A 3-dimensional figure whose base is a polygon
and whose other faces are triangles that share a
common vertex.
29
Geometry
Names of Solid Figures
A 3-dimensional figure with two circular bases
that are parallel and congruent.
30
Geometry
Names of Solid Figures
A 3-dimensional figure with one curved surface,
one flat surface (usually circular), one curved
edge, and one vertex.
31
Geometry
Names of Solid Figures
A solid figure made up of points that are all the
same distance from a point called the center.
32
Geometry
Parts of Solid Figures
A face of a solid figure is a flat surface.
An edge is a line segment where two faces meet.
A vertex is a point where two edges meet, or the
tip of a cone.
33
Geometry
Parts of Solid Figures
This figure has 6 faces, 12 edges, and 8 vertices.
The plural of vertex is vertices.
34
Geometry
Parts of Solid Figures
Some faces are called bases.
Prisms have two bases.
A pyramid has 1 base and a face for each side of
the base.
A cylinder has 2 circular faces which are bases.
35
Geometry
Solid Figures
If you could cut a prism or pyramid along some
edges, you could unfold the figure into a flat
shape. This is a pattern for the figure and it
is called a net.
It unfolds to look like this!
Triangular Pyramid
36
Geometry
Solid Figures
Here are some, but not all, nets for some prisms.
37
Geometry
Solid Figures
Here are some, but not all, nets for some
pyramids.
38
Geometry
Solid Figures
Figures that have the same shape and size are
congruent.
When two figures are congruent, you can place one
on top of the other and they will match exactly.
39
Geometry
Solid Figures
Congruent shapes can be turned and flipped.
40
Geometry
Solid Figures
In geometry, similar figures have the same shape.
Sometimes they are the same size. Sometimes
they are different sizes.
Similar
Not Similar
41
Geometry
Symmetry
Some figures can be folded in such a way that
the parts of the figure match exactly.
We say these figures have symmetry.
42
Geometry
Symmetry
The line where you fold the figure is called a
line of symmetry.
43
Geometry
Symmetry
A figure may have more than one line of symmetry.
A square has 4 lines of symmetry.
44
Geometry
Symmetry
Do the following figures have a line of symmetry?
NO
NO
NO
YES
YES
YES
45
Geometry
Transformations
When you slide a figure, it doesnt change in any
way except that it is now in a different place.
Another name for a slide is a translation.
46
Geometry
Transformations
When you flip a figure across a line, the new
figure looks like a reflection of the original
figure.
Another name for a flip is a reflection.
The line is called a line of reflection. The two
figures are mirror images of one another.
47
Geometry
Transformations
When you turn a figure, it spins around a point.
It looks different, but it is still congruent to
the original figure.
Another name for a turn is a rotation.
48
Geometry
Transformations
What type of transformation is being shown??
turn or rotation
slide or translation
turn or rotation
flip or reflection
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