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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.”
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
Geometry
.
A
Show arrowheads at
both ends to show that
the line goes on forever
.
B
a
The symbol for the
line has arrowheads,
just like the drawing
of the line.
in both directions.
WRITE: AB or BA or la
SAY: line AB or line BA
or line a.
Geometry
Types of lines:
HORIZONTAL LINES
.C
VERTICAL LINES
A horizontal line goes
straight across like the
horizon.
.D
A vertical line goes
straight down.
.E
.F
Geometry
More lines:
Intersecting lines:
.
A
.C
.
E
.D
.
Intersecting lines are lines
that cross. They cross at a
point.
For example, think about
streets that meet and cross at
intersections.
B
Line AB intersects line CD at
point E.
Geometry
More lines:
PERPENDICULAR LINES
When two intersecting lines meet to form square
corners, they are called perpendicular lines.
.M
.J
.K
.N
Line JK is perpendicular
to line MN.
A square corner is
a right angle.
Geometry
More lines:
PARALLEL LINES
Parallel lines are always the same distance
apart. They will never cross, or intersect,
one another, like railroad tracks.
.E
.G
.F
H
.
Line EF is parallel
to line GH.
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.
.
A
.
B
Line segment AB or
line segment BA.
Geometry
RAY A ray is a part of a line. It has one endpoint
and goes on forever in one direction.
.
O
.
Use the endpoint as the
B
endpoint
first letter when writing
the name of a ray.
When you see a little
Ray OB
One-headed arrow, say
“ray.”
Geometry
ANGLE
An angle is formed when two rays meet at
an endpoint.
The endpoint is called the vertex of the
angle.
.
.
A
Point B is the
vertex of the
angle.
B
.
C
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.”
A
B
.
C
Angle
ABC or angle
CBA
The vertex is
always written in
the middle.
Geometry
KINDS OF ANGLES
You can name angles by how the
measure compared to 90 degrees.
ACUTE ANGLES Acute angles measure less than
.
N
.
.
O
M
90 degrees.
Angle
MNO is less than 90
degrees so it is an ACUTE angle!
Geometry
KINDS OF ANGLES
You can name angles by how the
measure compared to 90 degrees.
OBTUSE ANGLES Obtuse angles measure greater
.
M
than 90 degrees.
.
N
.
O
Angle
MNO is greater than
90 degrees so it is an OBTUSE
angle!
Geometry
KINDS OF ANGLES
You can name angles by how the
measure compared to 90 degrees.
RIGHT ANGLES
Right angles measure exactly
90 degrees.
.
.
.
N
M
O
Angle
MNO is 90 degrees so
it is a right angle!
Geometry
KINDS OF ANGLES
STRAIGHT ANGLES
.
M
. .
N
O
A straight angle
measures 180
degrees. It looks
like a straight line.
Geometry
Polygons A polygon is a closed figure whose
sides are all line segments.
Polygons
Not Polygons
Geometry
Polygons The name of a polygon depends on the
number of sides it has.
triangle
quadrilateral
3 sides
pentagon
4 sides
5 sides
hexagon
octagon
6 sides
8 sides
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.
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.
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.
Geometry
Let’s look at just the parallelograms!
Each of these two parallelograms is also called a
rhombus.
A rhombus has all sides the same length.
Geometry
Let’s continue to just look at the parallelograms.
Each of these two parallelograms is also called a
rectangle.
A rectangle has 4 right angles.
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.
Geometry
A triangle is a polygon with three sides.
Triangles can be named two different ways.
First: Named by its angles.
Acute triangle
Right triangle
All angles
measure less
than 90
degrees.
One angle
measures
exactly 90
degrees.
Obtuse triangle
One angle
measures more
than 90
degrees.
Geometry
Triangles can be named two different ways.
Second: Named by the length of its sides.
Equilateral triangle
All sides are
the same
length.
Isosceles triangle
Scalene triangle
Two sides are
the same length.
Each side is a
different
length.
Geometry
Solid Figures
Solid figures have three dimensions: length,
width, and height.
Simple solid figure:
SPHERES
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.
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.
Geometry
Names of Solid Figures
A 3-dimensional figure with two circular bases
that are parallel and congruent.
Geometry
Names of Solid Figures
A 3-dimensional figure with one curved surface,
one flat surface (usually circular), one curved
edge, and one vertex.
Geometry
Names of Solid Figures
A solid figure made up of points that are
all the same distance from a point called
the center.
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.
Geometry
Parts of Solid Figures
This figure has 6 faces,
12 edges, and 8 vertices.
The plural of vertex is
vertices.
Geometry
Parts of Solid Figures
Some faces are called
bases.
Prisms have two bases.
A cylinder has 2 circular
faces which are bases.
A pyramid has 1 base and a
face for each side of the base.
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
Geometry
Solid Figures
Here are some, but not all, nets for some prisms.
Geometry
Solid Figures
Here are some, but not all, nets for some
pyramids.
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.
Geometry
Solid Figures
Congruent shapes can be
turned and flipped.
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
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.
Symmetry
Geometry
The line where
you fold the
figure is called a
line of symmetry.
Symmetry
Geometry
A figure may have more than one
line of symmetry.
A square has 4 lines of
symmetry.
Geometry
Symmetry
Do the following figures have a line of symmetry?
NO
NO
YES
YES
NO
YES
Geometry
Transformations
When you slide a figure,
it doesn’t change in any
way except that it is
now in a different place.
Another name for a
slide is a translation.
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.
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.
Geometry
Transformations
What type of transformation is being shown??
turn
slide
turn
flip
or
or
or
or
rotation
translation
rotation
reflection