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.

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Presentation transcript:

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.) 1 ST PERIOD3 RD PERIOD5 TH PERIOD6 TH PERIODTOTAL A B C D51017 F4304 Avg

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.

If an angle is 90 ° then it is a right angle. If you are a tourist at the Alamo, then you are in Texas.

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.

STATEMENT p=hypothesis q=conclusion EXAMPLE CONDITIONALIf p, then q If you are a guitar player, then you are a musician. CONVERSEIf q, then p If 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!

STATEMENTTRUE 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 FALSE X X A pair of non-adjacent supplementary angles

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.

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!

IF TIME PERMITS…. WHITE BOARD GROUP TRIVIA DIRECTIONS:RULES: Write the conditional, 1. NO TALKING. converse, inverse and 2. Every student must contrapositive statementsparticipate. on whiteboards quickly and3. 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