do now 12 – order of operations practice...

Geometry Level 2

Ms. Sheppard-Brick 617-596-4133

Do Now 12 Name: Date:

Do Now 12 – Order of Operations Practice 2

Simplify the following expressions.

1. 41650 •−

2. )2(8520 −−−−+−

3. )102(52)6( 2 −+−−

4. )5(151268−−+•

Geometry Week 5 Packet

Geometry Level 2


Conditional Statements Name: Date:

Conditional Statements – Guided Notes and Practice

A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in

the “then” clause. For instance, “If it snows, then they will cancel school.”

________________________________________ is the hypothesis.

________________________________________ is the conclusion.

Converse

To form the converse of the conditional statement, interchange the hypothesis and the conclusion. The converse of “If it snows, then they will cancel school” is _____________________

_____________________________________________________________________________

_____________________________________________________________________________

Example 1: Write the converse of each of the following statements.

a. If you are a student in this class, then you attend Lexington High School

b. If you are an athlete, then you play football.

Truth Value:

The truth value of a statement is true if it is always true and false if it is not always true.

Example 2: Write the converse of the following statement. Then determine whether each

statement is true or false.

1. True or False?

Statement If two angles are vertical, then they are congruent.

Converse ________________________________________


Geometry Level 2



Bi-conditional Statements

If both a statement and its converse are true, then we can write a bi-conditional statement using

the phrase “if and only if,” which is abbreviated “iff.”

Example 3: Rewrite the following statement and its converse as a bi-conditional statement in

two different ways.

Statement: If two angles have the same measure, then the angles are congruent.

Converse: If two angles are congruent, then the angles have the same measure.

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

Counterexamples:

A counterexample (as you know) is an instance that disproves a conjecture or statement.

Example 4: Write the converse of the following true statements and determine the truth-value of

the converse. If both are true, write a bi-conditional statement. If the converse is false, give a

counterexample.

a. If y = 3, then 2y – 1 = 5.

b. If you are a twin, then you have a sibling.


Geometry Level 2



Conditional Statements Stamp Race

Directions: Complete the following exercises. Each time you get to a stamp box, see a teacher to

have her check your work and stamp your paper.

Stamp Box


Geometry Level 2



Stamp Box

Stamp Box


Geometry Level 2

Homework 15 Name: Date:

Homework 15 – Deductive Reasoning and Conditional Statements

Directions: Identify the a) hypothesis and the b) conclusion of the conditional statement.

1. If two planes intersect, then their intersection is a line.

2. If ∠A is acute, then the measure of ∠A is between 0° and 90°.

3. If the sum of the measures of two angles is 180°, then the angles are supplementary.

4. If the measure of an angle is between 90° and 180°, then the angle is obtuse.

Directions: Rewrite the statement as a conditional statement.

5. Two angles that have the same measure are congruent angles.

6. Two angles that form a linear pair are supplementary angles.

7. An angle that has a measure of 90° is a right angle.

8. An angle that has a measure between 90° and 180° is an obtuse angle.

9. A dog with proper training will not misbehave.

Directions: Write the converse of each of the conditional statements, and then determine

whether the converse is true.

10. If two angles have the same measure, then the angles are congruent.

11. If two angles form a linear pair, then the angles are supplementary.

12. If the sum of the measures of two angles is 90° , then the angles are complementary.

13. If the measure of an angle is 90° , then the angle is a right angle.

For question 14, show your work and/or explain how you got your answer for each part of the

problem.

14. Paul wrote a true conditional statement that had a converse that was not true.

a. Write a statement that could be Paul’s statement.

b. Write the converse of Paul’s statement.

c. Explain why your answer to part a can be true without your answer to part be also being

true.


Geometry Level 2


Name: Date:

Relationships Between Lines – Guided Notes and Practice

Parallel Lines

Definition Notation

Figure Example

Perpendicular Lines

Definition Notation

Figure Example

Skew Lines

Definition Notation

Figure Example


Geometry Level 2


Name: Date:

Investigation:

Step 1: Fold a piece of patty paper to form a line.

Step 2: Fold the paper again by lining up the first fold.

Step 3: Unfold the paper and label the angles 1, 2, 3, and 4.

Step 4: Use a protractor to measure each of the angles. What do you notice?

Step 5: Tape or staple your paper to this sheet.

Right Angles Theorem: All Right Angles are Congruent

If:

Then:

If:

Then:

If:

Then:

BA

D

E

C

FBA

D

E

C

F


Geometry Level 2


Name: Date:

Perpendicular Lines Theorem: Perpendicular lines intersect to form four right angles.

If:

Then:

If:

Then:

If:

Then:

Congruent Adjacent Angles Theorem: Two lines that intersect to form adjacent congruent angles are perpendicular.

If:

Then:

If:

Then:

If:

Then:

A CD

B

E

A CD

B

E

F I

J

H

G

F I

J

H

G


Geometry Level 2


Name: Date:

Adjacent Acute Angles Theorem: If two sides of adjacent acute angles are perpendicular, then the angles are complementary.

If:

Then:

If:

Then:

If:

Then:

Example 1: Use your new theorems to determine what you can conclude about ∠1 𝑎𝑛𝑑 ∠2 in each figure. Name the theorem you used.

a.

b.

c.

21

L M

N

K

21

L M

N

K


Geometry Level 2


Name: Date:

Example 2: Use your new theorems to determine what you can conclude about ∠1 𝑎𝑛𝑑 ∠2 in each figure. Name the theorem you used.

a.

b.

c.

Example 3: Find the value of x, given that j ⊥ k.

a.

b.

c.


Geometry Level 2


Homework 16 Name: Date:

Homework 16 – Perpendicular Lines


do now 12 – order of operations practice...

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