Plane GeometryPlane GeometryPlane GeometryPlane Geometry

The building blocks of geometryThe 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”.