1. The building blocks of geometry
Plane Geometry
The building blocks of geometry

2. 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.

3. 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.

4. Congruent - figures that have the same size and shape
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”.

5. Types of angles

6. Acute angle - any angle which measures less than 90°

7. Right angle - any angle which measures exactly 90°

8. Obtuse angle - any angle which measures >90°, but <180°

9. Straight angle - any angle which measures exactly 180°

10. 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

11. Vertical angles – 2 angles formed by intersecting lines
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.

12. Complementary angles – 2 angles whose measures add up to 90°
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

13. Complementary angles

14. Supplementary angles – 2 angles whose measures add up to 180°
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.

15. Supplementary angles

16. 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.

17. Transversal – a line that intersects 2 or more lines
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.

18. Certain angle “names” describe “where” the angles are located
Certain angle “names” describe “where” the angles are located. Alternate interior angles are between the parallel lines. Alternate interior angles are congruent (equal)!

19. 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)!

20. 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)!

21. Adjacent angles create a straight angle or line
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.)

22. 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”.