Transcript All About Geometry

Angles
Polygons
Congruency
Symmetry
A branch of mathematics that deals
with the measurement, properties, and
relationships of points, lines, angles,
and two- and three-dimensional figures.
Understanding Vocabulary is Critical.
Visualizations Increase Understanding.
Lines of Symmetry
Lines of symmetry divide a figure into halves
That are reflections of each other
Size and Shape
Congruent figures have the same size and the
Means is
Same shape
congruent to
s
=
Size and Shape
Similar figures have the same shape and angles
Means is
But different sizes
s
similar to
Points, Lines, and Planes
Point
Point - A single location or
position.
Points, Lines, and Planes
Line
Line - All the points on a never-ending
straight path that extends in both
directions.
Points, Lines, and Planes
Line Segment
Line Segment - All the points on the
straight path between 2 points, including
those 2 points (endpoints).
Points, Lines, and Planes
Ray
Ray - A part of a line that extends
indefinitely in one direction.
Points, Lines, and Planes
Parallel Lines go in the same direction, the
Same distance apart. They never meet or cross
Points, Lines, and Planes
Intersecting Lines - Lines that meet at a point.
Points, Lines, and Planes
Perpendicular Lines - Lines that
meet to form right angles.
Points, Lines, and Planes
Plane
Plane - A flat surface that has
no edges or boundaries.
Angles
edge
The edges
meet at the
vertex
Protractors measure
angles in degrees
Angles
Right Angles = 90 Degrees
Angles
Acute Angle < 90 Degrees
Angles
Obtuse Angle >90
Angles
Straight Angle = 180 Degrees
Complementary Angles
If the sum of the
measures of two angles
is 90 degrees, they are
complementary angles
Supplementary Angles
If the sum of the
measures of two angles
is 180 degrees, they
are supplementary
angles
Midpoints and Bisectors
Midpoint of a Segment – A point that
divides the segment into two equal parts.
Midpoints and Bisectors
Perpendicular Bisector - A line, ray, or
plane that is perpendicular to a segment
and divides it into two equal parts.
Midpoints and Bisectors
25 Degrees
25 Degrees
Bisector of an Angle - A ray that
divides an angle into two congruent
angles.
Angle Relationships
A transversal is a line that intersects two
Parallel lines.
Transversal
Angle Relationships
When a transversal intersects two
parallel lines, eight angles are formed.
2
3
6
7
4
5
8
1
Angle Relationships
Angle 1 and 3 are examples of
vertical or opposite angles.
1
3
Vertical angles
are equal.
Angle Relationships
Angle 6 and 8 are examples of
vertical or opposite angles.
Vertical angles
are equal.
6
8
Angle Relationships
Angle 2 and 3 are examples of
supplementary angles.
2
3
Supplementary
angles equal
180 degrees
Angle Relationships
Angle 5 and 8 are examples of
supplementary angles.
5
8
Supplementary
angles equal
180 degrees
Angle Relationships
Angle 2 and 3 are examples of
corresponding angles.
2
6
Corresponding
angles are
equal.
Angle Relationships
Angle 4 and 8 are examples of
corresponding angles.
4
8
Corresponding
angles are
equal.
Angle Relationships
Angle 3 and 5 are examples of
alternate interior angles.
3
5
Alternate
interior angles
are equal.
Angle Relationships
Angle 4 and 6 are examples of
alternate interior angles.
4
6
Alternate
interior angles
are equal.
Angle Relationships
Angle 1 and 7 are examples of
alternate exterior angles.
1
7
Alternate
exterior
angles are
equal.
Angle Relationships
Angle 2 and 8 are examples of
alternate exterior angles.
2
8
Alternate
exterior
angles are
equal.
Transformations
Transformations are movements of
geometric figures
Transformations
ROTATION – A figure is turned about a
fixed point, called the center of rotation
(TURN)
Transformations
REFLECTION - A line acts like a mirror,
called the “line of reflection”
(FLIP)
Transformations
TRANSLATION - A movement (slide) of a
figure along a straight line.
(SLIDE)
Transformations
Dilation A transformation that changes
the size of an object, but not the shape