2.** Line:** An imaginary, undefined geometric term. A line is composed of connecting points. Think of the printout from your computer. If you draw a line and magnify it you will see connecting squares (points). A line is perfectly straight and extends indefinitely in two opposite directions.

3. **Plane:** An undefined geometric term composed of three non collinear points and the lines that connect them. Naturally two of these points are collinear, but the third point is part of a second line. The top of a desk represents part of a plane. Planes have length and width, but no depth; therefore they are imaginary. Like lines, planes extend indefinitely in all directions.

4. **Collinear:** Points that lie on a single line are collinear. "Co" means share or together.

5. **Coplanar**: Points that lie on a single plane are coplanar. Any three points are coplanar.

6. **Segment**: A segment is part of a line that begins at one point and ends at another.

7. **Endpoints**: Points on a line that define the beginning and end of a segment.

8. **Ray:** A ray is part of a line that begins at one point and extends indefinitely in one direction.

9. **Angle:** An angle consists of two rays that begin at a common endpoint. This endpoint is called the **vertex**** **of the angle. The rays are the *sides of the angle. *An angle divides a plane into two regions -- an interior region and an exterior region. Think of a clock. If the hour hand is on 12 and the minute hand is on 3, a 90 degree interior angle is formed and a 270 degree exterior angle is formed. If the hour hand is on 12 and the minute hand is on 11, a 330 degree interior angle is formed and a 30 degree exterior angle is formed.

10. ** Intersect**: If geometric figures have one or more points in common, the figures *intersect* at the point or points they share. The set of points that they share (or have in common) are called their intersection. Think of the intersection of streets.

11.** Postulates:** Fundamental geometric ideas that are accepted as true without proof. Postulates are also called "axioms."

12. **Length of segment AB**: Let A and B be points on a number line, with coordinates a and b. The measure of segment AB is called its length and is determined by calculating the absolute value of the difference of a and b.

13. **Number line:** A line that has been constructed and marked at evenly spaced intervals that correspond with the real numbers.

14. **Coordinate of a point:** A real number that corresponds with a point on a number line.

15. **Congruent**: Figures that have the same size and shape are said to be congruent. One of the figures can be rotated so that it is a vertical or horizontal image of the other and if its size and shape does not change, the figures are still congruent.

16. **Measure of an Angle:** Angles are measured in degrees as shown by coordinates of a half circle ranging from 0 to 180 degrees. A protractor is used to measure angles. The formula for finding angles is to subtract the coordinate of a point on one ray from the coordinate of the other ray and take the absolute value of the difference.

17. **Complementary angles**: Two angles whose measures have a sum of 90 degrees. Each angle is called the **complement** of the other.

18. **Supplementary angles**: Two angles whose measures have a sum of 180 degrees. Each angle is called the **supplement **of the other.

19. **Right angle**: An angle whose measure is 90 degrees.

20. ** Acute angle**: An angle whose measure is less than 90 degrees.

21. **Obtuse angle**: An angle whose measure is greater than 90 degrees, but less than 180 degrees.

22. ** Reflex angle**: An angle whose measure is greater than 180 degrees

23. **Straight angle**: An angle whose measure is 180 degrees. This is a straight line.

24. **Perpendicular lines** are two lines that intersect to form a right angle.

25. **Parallel lines** are two coplanar lines that do not intersect.

26. **Conjecture**: A statement that is an educated guess based on observation. These statements have not been proven.

27. ** Segment bisector**: A line that divides a segment into two congruent parts.

28. **Midpoint**: The point where a bisector intersects a segment.

29. **Perpendicular bisector**: A segment bisector that forms right angles with the line it bisects.

30. **Angle bisector**: A line or ray that divides an angle into two congruent angles.

31. **Inscribed circle**. A circle that is drawn inside another geometric figure and that touches it at one point on each of its sides. A circle inscribed in a triangle touches the triangle at one point on each of its three sides. "In" indicates inside.

32. **Incenter.** The center of an inscribed circle. It is the point where the angle bisectors of the geometric figure that contains the circle intersect.

33. **Circumscribed circle**. A circle drawn outside another geometric figure and touches the geometric figure on the outside of each of its corner points. "Circum" means around.

34. ** Circumcenter.** The center of a circumscribed circle. It is the point where the perpendicular bisectors of the sides of the geometric figure inside the circle intersect.

35. **Median**. Segments drawn from the midpoint of each side of a triangle to its opposite vertex. (The vertex of a triangle is the point where two lines come together to form an angle.)

36. ** ****Centroid**. The point in the center of the triangle where all three medians intersect.

37. ** Rigid Transformation**: Changing the position of an object without changing the shape or size of the object.

If P then Q or (Read p implies q)

Example:

Conditional statement: If a person is seventy years old, then the person is a senior citizen.

Converse statement: If a person is a senior citizen, then the person is seventy years old.

Notice that the converse is not necessarily true.

P if and only if Q or

Angles 1 and 2 above are adjacent angles.

Angles 1 and 2 above are vertical angles.

1* ***Definition of slope***: The slope of a non vertical line that contains point 1 (x, y) and point 2 ((x, y)) is equal to the ratio *.

unit 6:

2. ** Isometric drawing**: A drawing in which the horizontal lines of an object are represented by lines that form 30 degree angles with a horizontal line in the picture.

3. **Orthographic projection**: A view of an object in which points of the object are "projected" onto the picture plane along lines perpendicular to the picture plane.

4. **Polyhedron**: A closed spatial figure composed of polygons, call the faces of the polyhedron.

a. **Vertices:** The vertices of the faces are the vertices of the polyhedron

b. **Faces**: The polygons that make up the polyhedron

c. **Edges**: The place where two polygons meet.

c.** Skew**: Segments or rays of a polyhedron that are not parallel, yet would never meet if they were extended indefinitely.

d. **Regular polyhedron**: a polyhedron where all of the faces are congruent regular polygons, and the same number of polygons meet at each vertex. A cube is a regular polyhedron.

5. **Parallel planes**

Two planes are parallel if and only if they do not intersect (page 864).

6. **A line perpendicular to a plane**

A line is perpendicular to a plane if and only if it is perpendicular to every line in the plane that _______.

7.** A line parallel to a plane**

A line that is not contained in a given plane is parallel to the plane if and only if it is parallel to a line contained in the plane.

8. **Dihedral angle:** A dihedral angle is the figure formed by two half-planes with a common edge. Each half plane is called a face of the angle, and the common edge of the half-plane is called the

edge of the angle.

(Notice the half-plane includes the line.)

9. **Measure of a dihedral angle**.

The measure of a dihedral angle is the measure of an angle formed by two rays that are on the faces and that are perpendicular to the edge.

10. ** Right prism**: A prism in which all the lateral faces are rectangles. Remember that all the angles of a rectangle are right angles.

11. **Oblique prism**: A prism that has at least one non rectangular face. (See "prism" below)

12. **Diagonal of a right rectangular prism:**

In a right rectangular prism with dimensions l x w x h, the length of a diagonal is given by:

13. **Right-handed system**: The arrangement of the x, y, and z axis of three-dimensional coordinate planes.

14. ** Octants** (think about quadrants on a coordinate plane.) The x, y, and z axis of three-dimensional coordinate planes divide space into __eight octants__.

15. **Distance formula in three dimensions**

The distance, *d*, between the first point (x, y, z) and the second point (x, y, z) is given by

16. **Midpoint formula in three dimensions**. (This is just like the midpoint formula for two dimensions, but the z coordinates are included.)

The midpoint of a segment with endpoints at point 1 (x, y, z) and point 2 (x, y, z) is determined by taking one-half the sum of each corresponding coordinate point -- ((x+x)/2, (y + y)/2, (z + z)/2).

17. **Equation of a plane**.

Remember the standard form for the equation of a line is Ax+ By = C. The equation of a plane is similar with the z coordinate added. Ax + By + Cz = D where A, B, and C are real numbers and A is positive and is a whole number.

18. **Parametric equations** -- the instructions have different rules for each coordinate. They cannot be written in one equation, but in three separate equations for each coordinate.