TODAY IN GEOMETRY…

STATs for Ch.1 Test

Learning Goal: 2.2 Write definitions as Conditional Statements and use Deductive Reasoning to make logical arguments

Group Practice Activity Independent Practice – NO A.T.

Retake Ch. 1 Test before next Chapter test

HOW DID YOU “SHAPE” UP??Results for ALL of my Geometry classes:

GRADE NUMBER OF STUDENTS WHO TOOK THE CH.1 TEST(14 pts.)

1ST PERIOD 3RD PERIOD 5TH PERIOD 6TH PERIOD TOTAL

A 14 11 13 15 53B 5 9 6 4 24C 1 4 4 2 11D 5 1 0 1 7F 4 3 0 4 11

Avg. 29 28 23 26 105

CONDITIONAL STATEMENT: A mathematical statement given in if-then form.

if = hypothesis then = conclusion

Example: If two angles are a linear pair, then they are supplementary.

Test your knowledge:

Rewrite the conditional statement in if-then form:

1. All 90° angles are right angles.

2. because

3. When

4. Tourists at the Alamo are in Texas.

If an angle is 90° then it is a right angle.

If then .

If then .

If you are a tourist at the Alamo, then you are in Texas.

CONVERSE: To write the converse of a conditional statement, switch the hypothesis and conclusion.

Example: Conditional Statement:

Converse: .

NEGATION: Writing the opposite of the original statement.

EXAMPLE:Statement 1: Statement 2:The cat is black. The ball is not red.The cat is not black. The ball is red.

INVERSE: To write the inverse of a conditional statement, negate the hypothesis and conclusion.

EXAMPLE:Conditional Statement: If , then is obtuse.

Inverse: If , then is not obtuse.

CONTRAPOSITIVE: To write the contrapositive of a conditional statement, switch and negate the hypothesis and conclusion.EXAMPLE:Conditional Statement: If , then is obtuse.

Contrapositive: If is not obtuse then .

STATEMENT p=hypothesisq=conclusion EXAMPLE

CONDITIONAL If p, then qIf you are a guitar

player, then you are a musician.

CONVERSE If q, then pIf you are a musician

then you play the guitar.

INVERSE If not p, then not q

If you are not a guitar player, then you are

not a musician.

CONTRAPOSITIVE If not q, then not p

If you are not a musician, then you do

not play the guitar.

TRUTH VALUE: Whether a statement is true or false. If false, provide one counterexample.

EXAMPLE:Conditional statement: If an animal is a bird, then it has feathers. TRUE!

STATEMENT TRUE VALUE COUNTER-EXAMPLE

If two angles are a linear pair, then they are supplementary.

If two angles are supplementary, then they are a linear pair.

If two angles are not a linear pair, then they

are not supplementary

If two angles are not supplementary, then

they are not a linear pair

TRUE

TRUE

FALSE

FALSE

X

X

A pair of non-adjacent supplementary angles

A pair of non-adjacent supplementary angles

PRACTICE: Write a new conditional statement that follows from the pair of true statements:

1. If Rick takes chemistry this year, then Jesse will be Rick’s lab partner.

If Jesse is Rick’s lab partner, then Rick will get an A in chemistry.

2. If , then . If , then .

If , then .

If Rick takes chemistry this year, then Rick will get an A.

PERPEDICULAR LINES: Two lines are perpendicular if and only if they intersect to form a right angle. 𝑙

𝑚

Line l is perpendicular to line m

PRACTICE: Decide whether each statement about the diagram is true.

a.

b. and are a linear pair.

c. and are opposite rays.

𝐵

𝐴 𝐶

𝐷

𝐸

TRUE

FALSE

TRUE

BICONDITIONAL STATEMENT: an “if and only if” statement formed when a conditional and its converse statement is true.

EXAMPLE:Conditional Statement: If a polygon is regular, then it has equal sides and angles.

Converse: If a polygon has equal sides and angles then it’s a regular polygon.

Biconditional Statement: A polygon is regular if and only if it has equal sides and angles.

TRUE!

TRUE!

IF TIME PERMITS….

WHITE BOARD GROUP TRIVIA

DIRECTIONS: RULES:Write the conditional, 1. NO TALKING.converse, inverse and 2. Every student must contrapositive statements participate.on whiteboards quickly and 3. Cheating or talking =correctly. point deduction

1 POINT FOR EACH CORRECT ANSWER, 1 POINT FOR FIRST GROUP TO HAVE ALL CORRECT ANSWERS.

I will get my allowance if I do my homework.

CONDITIONAL: If I do my homework, then I will get my allowance.

CONVERSE: If I get my allowance, then I will do my homework.

INVERSE: If I don’t do my homework, then I won’t get my allowance.

CONTRAPOSITIVE: If I don’t get my allowance, then I won’t do my homework.

You give me $20, I will be your best friend.

CONDITIONAL: If you give me $20, then I will be your best friend.

CONVERSE: If I will be your best friend, then you will give me $20.

INVERSE: If you don’t give me $20, then I won’t be your best friend.

CONTRAPOSITIVE: If I won’t be your best friend, then you won’t give me $20.

A three sided polygon is a triangle.

CONDITIONAL: If a polygon has three sides, then it is a triangle.

CONVERSE: If a shape is a triangle, then it is a three sided polygon.

INVERSE: If a polygon does not have three sides, then it is not a triangle.

CONTRAPOSITIVE: If a shape is not a triangle, then it is not a three sided polygon.

Through any two points exists one line.

CONDITIONAL: If there is two points, then one line exists.

CONVERSE: If one line exists, then there is two points.

INVERSE: If there isn’t two points, then one line does not exists.

CONTRAPOSITIVE: If one lines does not exist, then there isn’t two points.

Two non-parallel lines intersect at a point.

CONDITIONAL: If there is two non-parallel lines, then they intersect at one point.

CONVERSE: If there is an intersection, then there is two non-parallel lines.

INVERSE: If there isn’t two non-parallel lines, then they don’t intersect.

CONTRAPOSITIVE: If there isn’t an intersection, then there isn’t two non-parallel lines.

The group with the most points will get a prize.

CONDITIONAL: If my group has the most points, then we will get a prize.

CONVERSE: If we get a prize, then my group has the most points.

INVERSE: If my group does not have the most points, then we will not get a prize.

CONTRAPOSITIVE: If we don’t get a prize, then my group does not have the most points.

HOMEWORK #1:

Pg. 82: 3-18, 26-28, 47-54