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

B

a

Geometry

Types of lines

A horizontal line goes straight across like the

horizon.

HORIZONTAL LINES

.

.

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.

Geometry

More lines

PERPENDICULAR LINES

When two intersecting lines meet to form square

corners, they are called perpendicular lines.

Geometry

More lines

PARALLEL LINES

Parallel lines are always the same distance

apart. They will never cross, or intersect, one

another, like railroad tracks.

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.

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

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.

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.

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.

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.

Geometry

KINDS OF ANGLES

You can name angles by how the measure compared

to 90 degrees.

RIGHT ANGLES

Right angles measure exactly 90 degrees.

Geometry

KINDS OF ANGLES

A straight angle measures 180 degrees. It looks

like a straight line.

STRAIGHT ANGLES

Geometry

Polygons

A polygon is a closed figure whose sides are all

line segments.

Not Polygons

Polygons

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

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

Lets look at just the parallelograms!

Each of these two parallelograms is also called a

rhombus.

A rhombus has all sides the same length.

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.

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.

Geometry

Triangles can be named two different ways.

Second

Named by the length of its sides.

Geometry

Solid Figures

Solid figures have three dimensions length,

width, and height.

Simple solid figure

CONES

SPHERES

CYLINDERS

PRISMS

PYRAMIDS

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 pyramid has 1 base and a face for each side of

the base.

A cylinder has 2 circular faces which are bases.

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.

Geometry

Symmetry

The line where you fold the figure is called a

line of symmetry.

Geometry

Symmetry

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

NO

YES

YES

YES

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.

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 or rotation

slide or translation

turn or rotation

flip or reflection