Lesson 5.4.notebook
December 03, 2012
Warm‐up
Write the converse of each statement. Then determine the truth value of the converse.
1) If two lines are parallel, then they do not intersect.
2) If x = ‐1, then x2 = 1.
1
Lesson 5.4.notebook
December 03, 2012
2
Lesson 5.4.notebook
December 03, 2012
3
Lesson 5.4.notebook
December 03, 2012
Lesson 5.4 ‐ Inverses, Contraposives, and Indirect Reasoning
The negaon of a statement has the opposite meaning of the original statement.
Ex 1: Write the negaon of each statement.
a) m<XYZ > 70
b) Today is not Wednesday.
4
Lesson 5.4.notebook
December 03, 2012
5
Lesson 5.4.notebook
December 03, 2012
In indirect reasoning, all possibilies are considered, then all but one are proved false.
An indirect proof is a proof involving indirect reasoning.
Wring an Indirect Proof
Step 1: State as an assumpon the opposite (negaon) of what you want to prove.
Step 2: Show that this assumpon leads to a contradicon.
Step 3: Conclude that the assumpon must be false and that what you want to prove must be true.
6
Lesson 5.4.notebook
Ex 3:
December 03, 2012
Write the first step in the indirect proof.
a) Prove: A triangle cannot contain two right angles.
b) Prove: m<A > m<B
Ex 4:
Idenfy the two statements that contradict each other.
a) I. P, Q, and R are coplanar
ll. P, Q, and R are collinear
lll. m<PQR = 60
b)
l. ΔABC is acute
ll. ΔABC is scalene
lll. ΔABC is equiangular 7
Lesson 5.4.notebook
December 03, 2012
Homework: Page 283 #1‐19, 22‐25, 34‐36
8
Lesson 5.4.notebook
December 03, 2012
The inverse of a condional statement negates both the hypothesis and the conclusion.
The contraposive of a condional switches the hypothesis and the conclusion and negates both.
Ex 2:
Write (a) the inverse and (b) the contraposive of Maya Angelou’s famous statement, “If you don’t stand for something, you’ll fall for anything.”
9