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.”
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
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.
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..
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.
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.
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
. .
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. .
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.”
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.
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.
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!
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
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
GeometryKINDS OF ANGLES
STRAIGHT ANGLES
M N O. . .
A straight angle measures 180 degrees. It looks like a straight line.
GeometryPolygons
A polygon is a closed figure whose sides are all line segments.
Polygons
Not Polygons
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
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.
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.
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.
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.
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.
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
GeometrySolid Figures
Solid figures have three dimensions: length, width, and height.
Simple solid figure:
PRISM
S CYLINDERS
CONES
PYRAMIDS
SPHERES
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.
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.
GeometryNames of Solid Figures
A 3-dimensional figure with two circular bases that are parallel and congruent.
GeometryNames of Solid Figures
A 3-dimensional figure with one curved surface, one flat surface (usually circular), one curved edge, and one vertex.
GeometryNames of Solid Figures
A solid figure made up of points that are all the same distance from a point called the center.
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.
GeometryParts of Solid Figures
This figure has 6 faces, 12 edges, and 8 vertices.
The plural of vertex is vertices.
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.
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!
GeometrySolid FiguresHere are some, but not all, nets for some
prisms.
GeometrySolid Figures
Here are some, but not all, nets for some pyramids.
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.
GeometrySolid Figures
Congruent shapes can be turned and flipped.
GeometrySolid FiguresIn geometry, similar figures have the same shape. Sometimes they are the same size. Sometimes they are different sizes.
Similar Not Similar
GeometrySymmetry
Some figures can be folded in such a way that the parts of the figure match exactly.
We say these figures have symmetry.
GeometrySymmetry
The line where you fold the figure is called a line of symmetry.
GeometrySymmetry
A figure may have more than one line of symmetry.
A square has 4 lines of symmetry.
GeometrySymmetry
Do the following figures have a line of symmetry?
NO NO NOYES
YES YES
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.
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.
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.
GeometryTransformations
What type of transformation is being shown??
turn
or
rotation
slide
or
translation
turn
or
rotation
flip
or
reflection