Geometry Rules!

Chapter 1 Notes

Notes #1: Section 1.3

Undefined Terms:

Point

Describe / Draw and Name / Real-life example

Line

Describe / Draw and Name and Symbol / Real-life example

Plane

Describe / Draw and Name / Real-life example

Defined Terms:

Examples:

Collinear points

Define / Draw and Name / Real-life example

Coplanar points

Define / Draw and Name / Real-life example

A postulate or axiom is…

Postulates and Theorems Relating Points, Lines, and Planes

Write
Through any two points there is exactly ______. / Draw
Write
If two lines intersect, then their intersection is a ______. / Draw / Use
Name the intersection of lines h and k.

Write
If two planes intersect, then their intersection is a ______. / Draw/Use
Name the intersection of planes M and N.




Write
______are needed to determine exactly one plane. / Draw/Use

Intersection…

Describe the intersection… / Draw and Name / Real-life example
of two lines
of a line and a plane
of two planes

Practice:

#1-4: True/False#5-7, complete each statement

1. l is in plane Y 5. name two planes that

meet at

2. planes X and Y

intersect at C

6. name three planes that

3. point B is in plane intersect at point A

X and Y

4. point C and l are 7. points A, B, F and ____

coplanarare coplanar

Algebra Practice: Simplify each expression. Write your answers as reduced fractions!

8.) 9.)

10) 11.) 12.)

Notes #2: Section1.4

A ____ to a statement is an example that shows that the statement is not true.

Example: Find one counterexample to show that each statement is false.

1. The quotient of two integers is not an integer.2. An even number cannot have 5 as a factor.

3. A number is always greater than its reciprocal.4. If a number is divisible by 5, then it is

divisible by 10.

More Defined Terms:

Examples:

Segment

Draw and Name / Real-life example

Ray

Draw and Name / Real-life example

Opposite Rays

Draw and Name / Real-life example

Parallel Lines

Draw and Name / Real-life example

Skew Lines

Describe / Draw and Name / Real-life example

Parallel Planes

Draw and Name / Real-life example

Practice: Use the diagram at the right to answer each of the following questions.

5. Name three labeled segments in the figure.

6. Name two rays in the figure.

7. Name two opposite rays.

8. Name all segments parallel to .

9. Name three segments that are skew to .10. Name two parallel planes.

Another defined term…

Length/Distance

Describe / Draw and Name / Real-life example

- Draw a number line; label two points “a” and “b”

- The distance, d, between these two points is ______

Use the formula to find the distance between the two points on a number line:

11) -3 and 412) -2 and -1113) 2.7 and 12.5

14.) What is the difference between AB and ?

Definition of Congruence

Write
If two segments have equal lengths, or two angles have the same measurement, then they are said to be ______segments and ______angles. / Draw & label using the congruence symbol / Use
15.) Measure these segments with your ruler; complete the equality statement and the congruence statement.

DE = ___________

Definition of Midpoint

Write
If M is the midpoint of , then
______= ______
______ ______
“midpoint”: / Draw / Use
16.) AB= 2x-3 and BC = 11. If B is the midpoint of AC, find x.

Algebra Practice: Simplify each expression. Don’t forget about the order of operations!!

17.) 18.)

19.)

Notes #3: Sections1.5

Definition of Segment Bisector

Write
If a segment, ray, or line is a bisector to a segment, then they intersect at the segment’s ______.
“bisect”: / Draw / Use

1.) bisects . What can you conclude based on the Definition of Segment Bisector?
2.) Using the definition of midpoint, what can you conclude next?

Segment Addition Postulate

Write
If B is between collinear points A and C, then
______+ ______= ______
“in between”: / Draw / Use

3.) If RS = 5 and ST = 9, find RT
4.) If RS = 7 – x, ST = 3x – 5, and
RT = 10, write an equation and solve for x.

5.) Name a situation in which we would use an equal sign (=) and a situation in which we would use a congruent sign () to state geometric relationships.

Write an equation and solve:

6.) DE = 3x – 5, EF = 5x – 9. Solve for x, DE, and EF.

Given: E is the midpoint of

7.) GE = y + 3, EH = 2y – 4, GH = 6y – 10. Solve for y, GE, EH, and GH. Using this information,

is E the midpoint of ?

8.) N is between collinear points A and B. If AB = 25, AN = 2x – 6, and NB = x + 7, find AN and NB .

9.) M is the midpoint of , RM = 5x + 9 and TM = 8x – 36. Find RM, MT, and RT.

10.) F is in between collinear points E and G. If EG = 75 and EF = 28, what is FG?

11.) F is in between collinear points E and G. If EG = 49, EF = 2x + 3, and FG = 4x – 2, find x. Then find EF and FG.

Algebra Practice: Solve each equation. Write your answers as reduced fractions, if necessary.

12. 13. 14.

15. 16.

Notes #4: Sections 1.6-1.7

More defined terms…

Angles:

Describe / Draw and Name
Vertex:
Sides: / Real-life example

Acute anglesRight anglesObtuse angles

Straight anglesCongruent anglesAdjacent angles

Vertical anglesComplementary anglesSupplementary angles

State another name for the given angle. If the picture is drawn to scale, is the given angle acute, right, obtuse, or straight,?

1.) 2.)

3.) 4.)

Using the figure at the right, answer each of the following questions.

5.) Name two supplementary angles.

6.) Name two vertical angles.

7.) Name two complementary angles.

8.) Name two congruent angles.

Angle Addition Postulate

Write
a)
If A lies in the interior of , then
______+ ______= ______
b)
If A lies in the interior of straight angle , then
______+ ______= ______ / Use
9.) If = 72°, solve for y, , and .

10.) Solve for m.

Perpendicular Lines

Describe / Draw and Name / Real Life Example

Definition of Angle Bisector

Write
If bisects , then
______= ______
______ ______ / Draw / Use
11.) bisects . Solve for a and .

Practice: Find the angle indicated.

12. bisects

13. Find the value of x in the diagram below if and .

14. bisects

Algebra Practice:Solve each equation. Write your answers as reduced fractions, if necessary.

Steps: 1.) Find the LCM of all of the denominators

2.) Multiply all terms in the equation by this numbers (denominators should cancel!)

3.) Solve new equation

15. 16.

17. 18.

Notes #5—Sections 1.7, 1.8, & Quiz Review

Complete the statement and name the properties you used: (some are used more than once)

1.) /
2.)
3.)If bisects , then X is the ______of .
4.)
5.) If XC = XD, then ____________/ 6.) m + ______= m
7.)

Parts to the coordinate plane: Label Quadrant I (QI), QII, QIII, QIV, x-axis, and y-axis

Plot and label the following points:

A(7, -3)B(-6, -1)C(0, 8)

D(-4, 0)E(5, 2)

Midpoint Formula
The midpoint of a segment connecting two points, and is:

(average the x’s, average the y’s)

Use the midpoint formula to find the midpoint of the segment with the given endpoints.

(Hint: first label your points as and

8.) (0, 2) and (6, 4) 9.) (-2, 6) and (4, 3)

10.) (a, 3) and (3a + 2, -1)

The midpoint M and one endpoint, A, of segment is given below. Find the coordinates of the second endpoint, B.

11.) M(4, -6) and A(2, -3)12.) M(1, 3) and A(8, 9)

13.) M(-1, 5) and A(1, 4)

Algebra Practice: Evaluate each expression.

14.) 15.)

16.) 17.)

Quiz Review:

Given the figure at the right, name the following:

18. two segments on Figure A

19. two rays on Figure A

20. two opposite rays on Figure A

21. two parallel segments on Figure B

22. two skew lines on Figure B

23. two parallel planes on Figure B

Figure B

What is the intersection of the following…

24. two distinct lines 25. two non-parallel planes26. a line & a plane that are not parallel

27. Given collinear points B & C and point F between them, find the value of x, BF, and CF if .

For #28-29, find the value of x.

28. B is the midpoint of and AC=9629.

For #30-31, use the figure at the right to find the value of the variable.

30.

31.

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