Transcript
Page 1: Geometry POINTA 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

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.”

Page 2: Geometry POINTA 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

GeometryLine

: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

Page 3: Geometry POINTA 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

Geometry

..A B a

Show arrowheads at

both ends to show that

the line goes on forever

in both directions.

WRITE: AB or BA or la

SAY: line AB or line BA or line a.

The symbol for the

line has arrowheads,

just like the drawing

of the line.

Page 4: Geometry POINTA 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

Geometry

Types of lines:

HORIZONTAL LINES

A horizontal line goes straight across like the horizon.

VERTICAL LINES A vertical line goes straight down.

.

.E

F

C D..

Page 5: Geometry POINTA 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

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..

.

..

.A

B

ED

C Line AB intersects line CD at point E.

Page 6: Geometry POINTA 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

Geometry

More lines:

PERPENDICULAR LINESWhen two intersecting lines meet to form

square corners, they are called perpendicular lines.

.

...

J

K

M N

A square corner is

a right angle.

Line JK is perpendicular to line MN.

Page 7: Geometry POINTA 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

Geometry

More lines:

PARALLEL LINES

Parallel lines are always the same distance apart. They will never cross, or intersect, one another, like railroad tracks.

Line EF is parallel to line GH.

. .E F

G H

. .

Page 8: Geometry POINTA 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

GeometryThink 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.

Line segment AB or line segment BA.

A B. .

Page 9: Geometry POINTA 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

GeometryRAY A ray is a part of a line. It has one

endpoint and goes on forever in one direction.

. .O B

endpoint

Use the endpoint as the

first letter when writing

the name of a ray.

Ray OB

When you see a little

One-headed arrow, say

“ray.”

Page 10: Geometry POINTA 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

GeometryANGLE An angle is formed when two rays

meet at an endpoint.

The endpoint is called the vertex of the angle.

...B

A

C

Point B is the vertex of the angle.

Page 11: Geometry POINTA 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

Geometry

...B

A

C

You can name an angle by writing the point on one ray, the vertex, and the point on the other ray.

Angle ABC or angle CBA

When you see a sharp corner symbol say “angle.”

The vertex is always written in the middle.

Page 12: Geometry POINTA 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

GeometryKINDS OF ANGLES

You can name angles by how the measure compared to 90 degrees.

ACUTE ANGLES

Acute angles measure less than 90 degrees.

...N

M

O

Angle MNO is less than 90 degrees so it is an ACUTE angle!

Page 13: Geometry POINTA 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

GeometryKINDS OF ANGLES

You can name angles by how the measure compared to 90 degrees.

OBTUSE ANGLES

Obtuse angles measure greater than 90 degrees.

Angle MNO is greater than 90 degrees so it is an OBTUSE angle!.

.

.M

NO

Page 14: Geometry POINTA 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

GeometryKINDS OF ANGLES

You can name angles by how the measure compared to 90 degrees.

RIGHT ANGLES Right angles measure exactly 90 degrees.

Angle MNO is 90 degrees so it is a right angle!.

..

M

N O

Page 15: Geometry POINTA 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

GeometryKINDS OF ANGLES

STRAIGHT ANGLES

M N O. . .

A straight angle measures 180 degrees. It looks like a straight line.

Page 16: Geometry POINTA 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

GeometryPolygons

A polygon is a closed figure whose sides are all line segments.

Polygons

Not Polygons

Page 17: Geometry POINTA 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

GeometryPolygonsThe 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

Page 18: Geometry POINTA 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

GeometryPolygons 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.

Page 19: Geometry POINTA 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

GeometryQuadrilaterals

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.

Page 20: Geometry POINTA 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

GeometryQuadrilaterals

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.

Page 21: Geometry POINTA 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

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.

Page 22: Geometry POINTA 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

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.

Page 23: Geometry POINTA 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

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.

Page 24: Geometry POINTA 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

One angle measures more than 90 degrees.

One angle measures exactly 90 degrees.

All angles measure less than 90 degrees.

Obtuse triangle

Right triangle

Acute triangle

GeometryA triangle is a polygon with three sides.

Triangles can be named two different ways.First: Named by its

angles.

Page 25: Geometry POINTA 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

Each side is a different length.

Two sides are the same length.

All sides are the same length.

Isosceles triangle

Equilateral triangle

Geometry

Triangles can be named two different ways.Second:

Named by the length of its sides.

Scalene triangle

Page 26: Geometry POINTA 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

GeometrySolid Figures

Solid figures have three dimensions: length, width, and height.

Simple solid figure:

PRISM

S CYLINDERS

CONES

PYRAMIDS

SPHERES

Page 27: Geometry POINTA 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

GeometryNames 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.

Page 28: Geometry POINTA 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

GeometryNames of Solid Figures

pyramids

A 3-dimensional figure whose base is a polygon and whose other faces are triangles that share a common vertex.

Page 29: Geometry POINTA 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

GeometryNames of Solid Figures

A 3-dimensional figure with two circular bases that are parallel and congruent.

Page 30: Geometry POINTA 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

GeometryNames of Solid Figures

A 3-dimensional figure with one curved surface, one flat surface (usually circular), one curved edge, and one vertex.

Page 31: Geometry POINTA 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

GeometryNames of Solid Figures

A solid figure made up of points that are all the same distance from a point called the center.

Page 32: Geometry POINTA 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

GeometryParts 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.

Page 33: Geometry POINTA 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

GeometryParts of Solid Figures

This figure has 6 faces, 12 edges, and 8 vertices.

The plural of vertex is vertices.

Page 34: Geometry POINTA 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

GeometryParts 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.

Page 35: Geometry POINTA 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

GeometrySolid 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.

Triangular Pyramid

It unfolds to look like this!

Page 36: Geometry POINTA 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

GeometrySolid FiguresHere are some, but not all, nets for some

prisms.

Page 37: Geometry POINTA 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

GeometrySolid Figures

Here are some, but not all, nets for some pyramids.

Page 38: Geometry POINTA 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

GeometrySolid FiguresFigures 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.

Page 39: Geometry POINTA 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

GeometrySolid Figures

Congruent shapes can be turned and flipped.

Page 40: Geometry POINTA 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

GeometrySolid FiguresIn geometry, similar figures have the same shape. Sometimes they are the same size. Sometimes they are different sizes.

Similar Not Similar

Page 41: Geometry POINTA 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

GeometrySymmetry

Some figures can be folded in such a way that the parts of the figure match exactly.

We say these figures have symmetry.

Page 42: Geometry POINTA 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

GeometrySymmetry

The line where you fold the figure is called a line of symmetry.

Page 43: Geometry POINTA 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

GeometrySymmetry

A figure may have more than one line of symmetry.

A square has 4 lines of symmetry.

Page 44: Geometry POINTA 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

GeometrySymmetry

Do the following figures have a line of symmetry?

NO NO NOYES

YES YES

Page 45: Geometry POINTA 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

GeometryTransformations 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.

Page 46: Geometry POINTA 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

GeometryTransformations 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.

Page 47: Geometry POINTA 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

GeometryTransformations 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.

Page 48: Geometry POINTA 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

GeometryTransformations

What type of transformation is being shown??

turn

or

rotation

slide

or

translation

turn

or

rotation

flip

or

reflection


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