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 

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
B
C
D
F
14
5
1
5
4
11
9
4
1
3
13
6
4
0
0
15
4
2
1
4
53
24
11
7
11
Avg.
29
28
23
26
105
CONDITIONAL STATEMENT: A
mathematical statement given in ifthen 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 ifthen form:
1. All 90° angles are right angles.
If an angle is 90° then it is a right angle.
2. 2𝑥 + 7 = 1 because 𝑥 = −3
If 𝑥 = −3 then 2𝑥 + 7 = 1.
2
3. When 𝑛 = 9, 𝑛 = 81
2
If 𝑛 = 9 then 𝑛 = 81.
4. Tourists at the Alamo are in Texas.
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: 𝐼𝑓 𝑚∠𝐴 = 99°,
𝑡ℎ𝑒𝑛 ∠𝐴 𝑖𝑠 𝑜𝑏𝑡𝑢𝑠𝑒.
Converse: 𝐼𝑓 ∠𝐴 𝑖𝑠 𝑜𝑏𝑡𝑢𝑠𝑒, 𝑡ℎ𝑒𝑛
𝑚∠𝐴 = 99°.
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 𝑚∠𝐴 = 99°,
then ∠𝐴 is obtuse.
Inverse: If 𝑚∠𝐴 ≠ 99°, then ∠𝐴 is not
obtuse.
CONTRAPOSITIVE: To write the
contrapositive of a conditional
statement, switch and negate the
hypothesis and conclusion.
EXAMPLE:
Conditional Statement: If 𝑚∠𝐴 = 99°,
then ∠𝐴 is obtuse.
Contrapositive: If ∠𝐴 is not obtuse then
𝑚∠𝐴 ≠ 99°.
p=hypothesis
q=conclusion
EXAMPLE
If p, then q
If you are a guitar
player, then you are a
musician.
CONVERSE
If 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.
If not q,
then not p
If you are not a
musician, then you do
not play the guitar.
STATEMENT
CONDITIONAL
CONTRAPOSITIVE
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
COUNTEREXAMPLE
If two angles are a
linear pair, then they
are supplementary.
TRUE
X
If two angles are
supplementary, then
they are a linear pair.
FALSE
A pair of non-adjacent
supplementary angles
If two angles are not a
linear pair, then they
are not supplementary
FALSE
A pair of non-adjacent
supplementary angles
If two angles are not
supplementary, then
they are not a linear pair
TRUE
X
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.
If Rick takes chemistry this year, then Rick will get an A.
2.
If 𝑥 2 > 25, then 𝑥 2 > 20.
If 𝑥 > 5, then 𝑥 2 > 25.
If 𝑥 > 5, then 𝑥 2 > 20.
PERPEDICULAR LINES: Two lines are
perpendicular if and only if they
intersect to form a right angle.
𝑙
Line l is perpendicular
to line m
𝑚
𝒍⊥𝒎
PRACTICE: Decide whether each statement about the
diagram is true.
a. 𝐴𝐶 ⊥ 𝐵𝐷
𝐵
TRUE
b. ∠𝐴𝐸𝐵 and ∠𝐶𝐸𝐵 are
a linear pair.
TRUE
c. 𝐸𝐴 and 𝐸𝐵 are
opposite rays.
FALSE
𝐴
𝐸
𝐷
𝐶
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. TRUE!
Converse: If a polygon has equal sides and angles then it’s a
regular polygon. TRUE!
Biconditional Statement: A polygon is regular if and only if it
has equal sides and angles.
IF TIME PERMITS….
WHITE BOARD GROUP TRIVIA
DIRECTIONS:
Write the conditional,
converse, inverse and
contrapositive statements
on whiteboards quickly and
correctly.
RULES:
1. NO TALKING.
2. Every student must
participate.
3. Cheating or talking =
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 nonparallel 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