Geometry
10409
Semester 1
Students must complete the following to receive full credit for EACH credit/unit:
Terms Define all terms, give examples when appropriate
Notes 10 Bullet Points from each section or 3-5 sentence summaries from each section
Questions Answer the questions completely
Test Take each test found at: https://testmoz.com/class/16400
All test passwords are: osc
All videos have Spanish translations under the play button.
Todos los videos tienen traducción al español debajo del botón de reproducción.
Unit 1 - Basics of Geometry
Terms to Know:
Terms to Know:
acute angle
adjacent angles
angle
angle bisector
axiom
collinear points
complementary angles
congruent angles
congruent segments
construction
coordinate
coplanar points
defined terms
distance
endpoints
exterior of an angle
interior of an angle
intersection
line
line segment
linear pair
midpoint
obtuse angle
opposite rays
plane
point
postulate
ray
right angle
segment
segment bisector
sides of an angle
straight angle
supplementary angles
undefined terms
vertex of an angle
vertical angles
Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.
Section 1.1: Points, Lines, and Planes
Section 1.2: Measuring and Constructing Segments
Section 1.3: Using Midpoint and Distance Formulas
Section 1.4: Perimeter and Area in the Coordinate Plane
Section 1.5: Measuring and Constructing Angles
Section 1.6: Describing Pairs of Angles
Important Questions: Answer the following Questions
Use the diagram above for Questions 1-7.
1. Give two names for the plane.
2. Name three collinear points.
3. Name three coplanar points.
4. Name three points.
5. Name one ray.
6. Name two lines.
7. Name one line segment.
8. Find the distance between the two points S(-5, -2) and T(-3, 4).
Find the angle measure.
9. Angle B is a supplement of Angle A and the measurement of Angle A = 65.2°. Find the measurement of Angle B.
10. Angle B is a complement of Angle A and the measurement of Angle A = 65.2°. Find the measurement of Angle B.
Take the Geometry Unit 1 Test at https://testmoz.com/class/16400
Unit 2 - Reasoning and Proofs
Terms to Know:
Terms to Know:
biconditional statement
conclusion
conditional statement
conjecture
contrapositive
converse
counterexample
deductive reasoning
equivalent statements
flowchart proof (flow proof)
hypothesis
if-then form
inductive reasoning
inverse
line perpendicular to a plane
negation
paragraph proof
perpendicular lines
proof
theorem
truth table
truth value
two column proof
Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.
Section 2.1: Conditional Statements
Section 2.2: Inductive and Deductive Reasoning
Section 2.3: Postulates and Diagrams
Section 2.4: Algebraic Reasoning
Section 2.5: Proving Statements About Segments and Angles
Section 2.6: Proving Geometric Relationships
Important Questions: Answer the following Questions
Describe the pattern. Then write the next two numbers or figures.
1, 4, 9, 16, 25, ...
Rewrite the conditional statement in if-then form. Then write the converse, inverse, and contrapositive of the conditional statement. Decide whether each statement is true or false.
2. It is noon when the clock strikes 12.
3. An angle measure of 87° is an acute angle.
4. The month of November is after December.
Write the converse and inverse of the statement.
5. If it is Sunday, then it is the weekend.
6. If an animal is a bird, then it has two eyes.
Find a counterexample to show that the conjecture is false.
7. The difference of a positive number and a negative number is always positive.
8. If a triangle measures 180°, each angle is 60°
Decide whether inductive reasoning or deductive reasoning is used to reach the conclusion.
9. Gas prices have gone up every day this week. The price of gas will go up tomorrow.
10. What goes up must come down. The ball went up. It will come down.
Take the Geometry Unit 2 Test at https://testmoz.com/class/16400
Unit 3 - Parallel and Perpendicular Lines
Terms to Know:
Terms to Know:
alternate exterior angles
alternate interior angles
consecutive interior angles
corresponding angles
directed line segment
distance from a point to a line
parallel lines
parallel planes
perpendicular bisector
skew lines
transversal
Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.
Section 3.1: Pairs of Lines and Angles
Section 3.2: Parallel Lines and Transversals
Section 3.3: Proofs With Parallel Lines
Section 3.4: Proofs With Perpendicular Lines
Section 3.5: Equations of Parallel and Perpendicular Lines
Important Questions: Answer the following Questions
Use the Diagram above to Identify all pairs of angles of the given type for Questions 1-5.
1. consecutive interior
2. alternate interior
3. corresponding
4. alternate exterior
5. vertical
Complete the sentence.
6. The slopes of perpendicular lines are _______________.
7. Parallel lines have the _______________ slope.
8. The shortest distance from any point to a line is a _______________.
Determine which lines, if any, are parallel or perpendicular.
9. Line a: y = 5x - 6
Line b: x + 5y = 5
10. Line a: 2x + y = 10
Line b: -6x - 3y = 3
Line c: x - 2y = 8
Take the Geometry Unit 3 Test at https://testmoz.com/class/16400
Unit 4 - Transformations
Terms to Know:
Terms to Know:
angle of rotation
center of dilation
center of rotation
center of symmetry
component form
composition of transformations
congruence transformation
congruent figures
dilation
enlargement
glide reflection
horizontal component
image
initial point
line of reflection
line symmetry
line of symmetry
preimage
reduction
reflection
rigid motion
rotation
rotational symmetry
scale factor
similar figures
similarity transformation
terminal point
transformation
translation
vector
vertical component
Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.
Section 4.1: Translations
Section 4.2: Reflections
Section 4.3: Rotations
Section 4.4: Congruence and Transformations
Section 4.5: Dilations
Section 4.6: Similarity and Transformations
Important Questions: Answer the following Questions
The graph above shows quadrilateral ABCD. Which set of vertices represents a rotation? a glide reflection? a translation? a similarity transformation? Write a rule for each of these transformations.
1. A'(-3, 1), B'(-1, 4), C'(-3, 6), D'(-6, 3)
2. A'(-5, -5), B'(-3, -8), C'(-5, -10), D'(-8, -7)
3. A'(-8, 0), B'(-4, -6), C'(-8, -10), D'(-14, -4)
4. A'(1, -3), B'(4, -1), C'(6, -3), D'(3, -6)
5. A'(-1, -3), B'(-4, -1), C'(-6, -3), D'(-3, -6)
6. A'(6, 1), B'(8, 4), C'(6, 6), D'(3, 3)
Determine whether the polygons with the given vertices are congruent. Use transformations to explain your reasoning.
7. A(8, -6), B(1, -3), C(1, -9), and D(-7, 1), E(0, -2), F(0, 4)
8. J(-4, 1), K(-10, 3), L(-10, 9), M(-4, 7) and N(4, 2) O(2, -8), P(-4, -8), Q(-2, 2)
9. Identify the line symmetry (if any) of the word CHECKBOOK?
10. Find the component form of the vector that translates P(4, 5) to P'(-3, 7).
Take the Geometry Unit 4 Test at https://testmoz.com/class/16400
Unit 5 - Congruent Triangles
Terms to Know:
Terms to Know:
base angles of an isosceles triangle
base of an isosceles triangle
coordinate proof
corollary to a theorem
corresponding parts
exterior angles
hypotenuse
interior angles
legs of an isosceles triangle
legs of a right triangle
vertex angle
Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.
Section 5.1: Angles of Triangles
Section 5.2: Congruent Polygons
Section 5.3: Proving Triangles Congruence by SAS
Section 5.4: Equilateral and Isosceles Triangles
Section 5.5: Proving Triangles Congruence by SSS
Section 5.6: Proving Triangles Congruence by ASA and AAS
Section 5.7: Using Congruent Triangles
Section 5.8: Coordinate Proofs
Important Questions: Answer the following Questions
Use the Graphic above to find the measure of the missing angles for Questions 1-5.
1. Measure of Angle 1
2. Measure of Angle 2
3. Measure of Angle 3
4. Measure of Angle 4
5. Measure of Angle 5
Given that PQRS is equivalent to WXYZ, find the corresponding parts.
6. Angle P is congruent to
7. Line Segment RS is equivalent to
8. Line Segment XY is equivalent to
9. Angle Y is congruent to
10. Line Segment PS is equivalent to
Take the Geometry Unit 5 Test at https://testmoz.com/class/16400