Geometry Unit 2 Review Day 1 What to expect on...

AB Unit 2 full review with mt.notebook October 06, 2016

Geometry Unit 2 Review Day 1

What to expect on the test:• Conditional Statements

• Converse

• Inverse

• Contrapositive

• Bi-conditional statements

• Counterexamples/Instances

• Converse of parallel lines conjecture

• Algebraic proofs and their properties

• Geometric proofs

Today we are going to

do more work with

Algebraic Proofs

A. Addition PoEB. Subtraction PoEC. Multiplication PoED. Division PoEE. Distributive PoEF. Substitution PoEG. Transitive PoEH. Symmetric PoEI. Reflexive PoE

Name the Property of Equality (PoE) that justifies each statement.

*If a = b, then b = a

*xy = xy

*If A = C and M = E, then A+M = C+E

H. Symmetric PoE

I. Reflexive PoE

A. Addition PoE




*If A + B = 90 and A = 30, then 30 + B = 90

*x + 3 = 17, then x = 14

*If 7x = 42, then x = 6.

F. Substitution PoE

B. Subtraction PoE

D. Division PoE



*2(x + 4) = 2x + 8

*If x = y + 3 and y + 3 = 10, then x = 10.

*Suppose Abdi's height = Juan's height and Juan's height = Marissa's height, then Abdi's height = Marissa's height.

E. Distributive PoE

G. Transitive PoE

G. Transitive PoE


Name the PoE that justifies each statement

Given:

Prove: Statement Reason

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.


Given:

Prove:

Statement Reason

1. 1.

2. 2.

3. 3.

4. 4.



Given:

Prove:

Statement Reason

1. 1.

2. 2.

3. 3.


Given:


1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.


Fill in the reasons and name the PoE that justifies each statementGiven:


1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

Conditional Statements:If a polygon is a hexagon, then it has six sides.

Write the converse. Is it true or false?

Write the inverse. Is it true or false?

Write the contrapositive. Is it true or false?

Write it as a biconditional statement.


What are the three undefined terms in geometry?

Why are they undefined?

What's the difference between an axiom (postulate), definition, and theorem?


Euclid (a famous and very influential mathematician) began the study of Geometry by making statements such as: “A straight line can be drawn between any two points.” No one is able to prove this so they just accept it to be true. Is this statement a theorem or an axiom(postulate)? Explain your reasoning.

Multiple Choice: Decide which of the following sketches of triangle ABC depicts an instance and which one shows a counterexample for the following statement. Provide one answer for the instance and one answer for the counterexample.

_______ Instance _______ Counterexample


Find a counterexample to the statement:

• If two angles are complementary, then the angles are both 45o.

• The square of a number is larger than that number

• If a polygon has four sides, then it is a square.

• If you live in Minnesota, then you live in Minneapolis.

78o

102o

Are lines p and q parallel?

p

q


Which lines are // if...

Geometric proof #1

Given:

Prove:

What do you see? Math?

Two-Column Proof Statement Reason

1.

2.

3.

4.

a

b

t

1

23


Geometric proof #2

Given:

Prove: What do you see? Math?

Two-Column Proof Statement Reason

1.

2.

3.

4.

I G

12

P

3 4

C

O W

1.

2.

3.

4.

5.

6.

1. Given

2. Definition of congruent angles

3. Angle Addition Postulate

4. Substitution PoE

5. Subtraction PoE

6. Definition of congruent angles

Geometric proof #2 Answer


Good luck on your test! You WILL do great!

Geometry Unit 2 Review Day 1 What to expect on...

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