Plane Geometry
The building blocks of geometry
Geometry plays an important part of many types of
careers from engineers to carpenters. Here is the
Cooper River Bridge in Charleston SC. This bridge
would not be possible without geometry.
Points, lines, and planes:
Here are
some definitions you will need to remember.
• Point – names an exact location on a plane.
• Line – a collection of points forming a straight path
that extends infinitely in opposite directions.
• Plane – a perfectly flat surface that extends forever
in all directions.
• Segment – part of a line between two endpoints.
• Ray – part of a line that starts at one endpoint and
extends forever in one direction.
• Angle – formed by 2 rays with a common endpoint
called a vertex. Pleural of vertex is vertices.
Congruent - figures that have the same size
and shape.
Segments that have the same length are
congruent.
Angles that have the same measure are
congruent.
The symbol for congruence is  , which is read
“ congruent to”.
Types of angles
Acute angle -
any angle which measures
less than 90°
Right angle -
any angle which measures
exactly 90°
Obtuse angle -
any angle which
measures >90°, but <180°
Straight angle -
any angle which
measures exactly 180°
The definitions up until now apply to angles
when we look at one angle alone, but there are
also some special relationships between pairs
of angles
Adjacent angles – 2
angles which share a
vertex, share a side
but do not overlap.
Angle 1 and angle 2 are
adjacent angles.
Angle 1 and angle ABC
are not adjacent
Vertical angles – 2 angles
formed by intersecting
lines. They can not be
adjacent, and they are
always equal in measure.
They are across from one
another.
Angle 1 and angle 3 are
vertical angles.
Angle 2 and angle 4 are
vertical angles.
Angle 1 and angle 2 are not
vertical.
Complementary angles –
2 angles whose measures
add up to 90°.
Complementary angles
can be placed so that
they form perpendicular
lines.
Angle 1 and angle 2 are
complementary.
Angle XYZ and angle 1
are not complementary.
Line segment XY is
perpendicular to line
segment YZ
Complementary angles
Supplementary angles – 2 angles whose
measures add up to 180°. Supplementary
angles can be placed so that they form a
straight line.
Angle 1 and angle 2 are supplementary.
The line passing through points A, B, and C is a
straight line.
Supplementary angles
Parallel lines and angles
Angles formed by parallel lines and transversals
(lines intersecting parallel lines), have a very
interesting relationship.
The most important angles needed for most math
applications are called alternate interior angles,
alternate exterior angles and corresponding
angles.
Transversal – a line that intersects 2 or more
lines.
Corresponding angles – angles formed by a
transversal that are in the same relative position.
Alternate interior angles – a pair of angles on
the inner sides of two lines cut by a transversal
and are on opposite sides of the transversal.
Alternate exterior angles – a pair of angles on
the outer sides of two lines cut by a transversal
and are on opposite sides of the transversal.
Adjacent angles – angles that share a common
vertex and a side.
Certain angle “names” describe “where” the
angles are located.
Alternate interior angles are between the
parallel lines.
Alternate interior angles are congruent (equal)!
Alternate exterior angles can be easily found
because their “name” describes “where” they are.
Alternate exterior angles are outside the parallel
lines.
Alternate exterior angles are congruent (equal)!
Corresponding angles are on the same side of
the transversal, one is interior and the other
is exterior and they are not adjacent (they
don’t touch).
Corresponding angles are congruent (equal)!
Adjacent angles create a straight angle or line.
Since a straight angle is 180°, adjacent angles
add up to 180°. (Adjacent angles share a
vertex, share a side, and do not overlap.)
Knowing these few facts
about lines and their
relationships will help you
solve many problems dealing
with angles and geometry.
Did you know the word
geometry comes from a
Greek word meaning “to
measure the earth”.