6.3 Basic Facts About Parallel Planes
Obj.: To recognize lines parallel to planes, parallel planes, and skew lines. To use
p roperties relating parallel lines and planes.
Warm-Up:
Notes:
A line and a plane are parallel if they do not intersect.
Two planes
2.1 Perpendicularity
Obj.: To recognize the need for clarity and concision in proofs. To understand the
c oncept of perpendicularity.
Warm Up: Go over test.
Notes:
perpendicular - lines, rays, or segments that intersect at right angles.
Example 1 Write a
1.9 Probability
Obj.: To solve probability problems.
Warm Up: Answer the questions below.
A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble
is chosen at random from the jar, find each probability.
a. P(red)
b. P(yellow)
1.7 Deductive Structure
1.8 Statements of Logic
Obj.: To identify undefined terms, postulates, definitions, and theorems. To
recognize that geometry is based on a deductive structure. To recognize conditional
s tatements, the converse, the inverse, and th
1.5 Division of Segments and Angles
O bj.: To identify midpoints and bisectors of segments. To identify trisection points
a nd trisectors of segments. To identify angle bisectors and angle trisectors.
Warm Up: Fill in the blank with always, sometimes, or
1.4 Beginning Proofs
C
O bj.: To write simple two-column proofs.
A
Warm Up: Classify each statement as true or false.
1. is in plane R.
2. Plane S contains .
D
3. Plane R and plane S contain D.
4. D is on line h.
h
R
5. h is in plane S.
6. h is in plane R
1.2 Measurement of Segments and Angles
Obj.: To measure segments and angles. To classify angles by size. To measure an
a ngle using DMS. To recognize congruent angles and segments.
Warm Up: Name all angles in the diagram.
Notes:
Go over measuring segments
1.1 Getting Started
Obj.: To recognize points, lines, line segments, rays, angles, and
t riangles.
Warm Up: How many squares are there in the 4 x 4 square in the diagram?
Notes:
point - represented by a dot. Use a capital letter to name a point.
line - li
Geometry Honors
Chapter 1 Review
Name _
Date _ Pd. _
For problems #1 - #6, answer each question based on the diagram.
B
1. Name an obtuse angle.
60
C
40
2. If , then .
3. How many angles have a vertex at A? _
G
4A Is70 _
.?
80
5.
_
30
6.
D
_
F
30
E
7.
Geometry Honors
Chapter 7 Review
Name _
Date _ Pd. _
IMPORTANT FORMULAS
Sum of the measures of the interior angles of a polygon
Sum of the measures of the exterior angles of a polygon
Number of diagonals of a polygon
Measure of each interior angle of a re
Geometry Honors
Chapter 1 Review
Name _
Date _ Pd. _
For problems #1 - #6, answer each question based on the diagram.
B
1. Name an obtuse angle.
60
C
40
2. If , then .
3. How many angles have a vertex at A? _
G
4A Is70 _
.?
80
5.
_
30
6.
D
_
F
30
E
7.
Geometry Honors
Chapter 2 Review
Name _
Date _ Pd. _
I. In problems 1 5, decide if each statement is true or false.
1. On a two-dimensional coordinate system, the point (0,0) is called the center. _
2. The complement of an acute angle is obtuse. _
3. If t
Geometry Honors
Chapter 4 Review
Name _
Date _ Pd. _
I. In problems 1 6, write if each statement is true or false.
1. If two lines intersect to form two congruent, adjacent angles, then the lines are perpendicular.
_
2. If two points, and , are equidistan
2.5 Addition and Subtraction Properties
Obj.: A pply the addition properties of segments and angles. To apply the
s ubtraction properties of segments and angles.
Warm-Up: If the complement of an angle is 40 less than its supplement, find the
angle.
Notes:
2.2 Complementary and Supplementary Angles
Obj.: To recognize complementary and supplementary angles.
Warm Up: If , find each.
a.
b.
c.
Notes:
complementary angles - two angles whose sum is . Each of the two angles is
called the complement of the other.
s
2.6 Multiplication and Division Properties
Obj.: A pply the multiplication properties of segments and angles. To apply the
d ivision properties of segments and angles.
Warm-Up: Given all the following below to be true, find
is complementary to
is compleme
2.8 Vertical Angles
Obj.: To recognize opposite rays. To recognize vertical angles.
Warm-Up: By how much does x exceed y? 110
x - 2y
x + 2y
50
Notes:
Opposite rays - two collinear rays that have a common endpoint and extend in
different directions.
Verti
Geometry Honors
Chapter 4 Review
Name _
Date _ Pd. _
I. In problems 1 6, write if each statement is true or false.
1. If two lines intersect to form two congruent, adjacent angles, then the lines are perpendicular.
_
2. If two points, and , are equidistan
4.4 The Equidistance Theorems
Obj.: To recognize the relationship between equidistance and perpendicular
b isection.
Warm-Up:
Notes:
Distance the length of the shortest path joining two objects.
Postulate A line segment is the shortest path between two po
4.6 Slope
Obj.: To understand the concept of slope. To relate the slope of a line to its
o rientation in the coordinate plane. To recognize the relationships between the
s lopes of parallel and perpendicular lines.
Warm-Up: Draw the line through and
on a
4.1 Detours and Midpoints
Obj.: To apply the midpoint formula.
Warm-Up:
Notes:
Midpoint Formula If and , then the midpoint of can be found by using the
midpoint formula:
Example 1 Find the coordinates of M, the midpoint of with and .
Example 2 In , find t
3.7 Angle-Side Theorems
Obj.: To apply theorems relating the angle measures and side lengths of triangles.
A
Warm-Up: Write a two column proof.
Given:
is a median of
M
Prove:
T
N
Notes:
Theorem If two sides of a triangle are congruent, then the angles opp
3.8 The HL Postulate
F
Obj.: To use the HL postulate to prove right triangles congruent.
Warm-Up: Write a two column proof.
A
Given:
D
B
E
Prove:
C
Notes:
HL Postulate If there exists a correspondence between the vertices of two right
triangles such that
3.6 Types of Triangles
Obj.: To name the various types of triangles and their parts.
F
Warm-Up: Write a two-column proof.
A
Given:
B
E
D
Prove:
C
Notes:
Classifying Triangles:
By sides:
1. Equilateral Triangle
2. Isosceles Triangle
3. Scalene Triangle
3.5 Overlapping Triangles
Obj.: To use overlapping triangles in proofs.
T
P
Warm-Up: Write a two column proof.
Given:
W
S
Prove:
M
Notes:
A
Example 1 Write a two-column proof.
Given:
E
D
Prove:
B
C
Example 2 Write a two-column proof.
M
F
Given:
G
K
H
J
G
3.3 CPCTC and Circles
Obj.: To apply the principle of CPCTC. To recognize some basic properties of
c ircles.
Warm-Up:M
Given:
S
Prove:
W
F
Notes:
CPCTC Corresponding Parts of Congruent Triangles are Congruent
Introduction to Circles
P
A
C
B
Theorem All ra
Geometry Honors
Chapter 3 Review
Name _
Date _ Pd. _
I. In problems 1 5, write if the statement is always true, sometimes true, or never true.
1. A scalene triangle is obtuse. _
2. An altitude of a triangle is perpendicular to the side to which it is draw
2.7 Transitive and Substitution Properties
Obj.: A pply the transitive properties of segments and angles. To apply the
s ubstitution property.
Warm-Up:
Notes:
Theorem - If angles (segments) are congruent to the same angle (segment) then
they are congruent
Geometry Honors
_
Chapter 5 Review
_
Name
Date _ Pd.
Both pairs of opposite sides
are parallel.
Exactly one pair of opposite
2.
sides are parallel.
1.
3. Diagonals are perpendicular.
4. Diagonals are congruent.
5. Diagonals bisect each other.
Both pairs o