Homework: pg 83;
16-21 and 25-29
Warm up
1. Re-write the following statements as an if-then
statement.
2. State the converse of the statement.
a. The midpoint of a segment is a point that divides the
segment into two congruent segments
b. Two angles are complementary if the sum of their
measures is 90 degrees
c. In an equilateral polygon, all sides are congruent
Converse- inverse- contrapositive
Ex: if water is frozen, then its temperature is below 0⁰C.
Converse- exchange the hypothesis and the conclusion
Ex- if the water temperature is below 0 ⁰C, then it is frozen
Inverse- negate both the hypothesis and the conclusion
Ex: If water is not frozen, then its temperature is not below 0 ⁰C
Contrapositive- negate the hypothesis and conclusion of the converse
Ex: if the water temperature is not below 0 ⁰C, then it is not frozen
Hmwk-pg 83; 7-10
7) Complementary angles add to 90 degrees
If-then _____________________________________________________
Converse ___________________________________________________
Inverse _____________________________________________________
Contrapositive _______________________________________________
9) 3x + 10 = 16, because x = 2
If-then _____________________________________________________
Converse ___________________________________________________
Inverse _____________________________________________________
Contrapositive _______________________________________________
Guitar players are musicians…
If-then
Converse
Inverse
Contrapositive
True/false?
With a partner…
If a polygon is equilateral, then it is regular.
ConverseInverseContrapositiveEquivalent statements- both are true or both are false
Biconditional statements
• When a conditional statement and the
converse are both true
• Use the phrase “if and only if”
• Ex: If two lines intersect to form a right angle,
then they are perpendicular lines
• Converse• Biconditional- two lines are perpendicular
_____________ they intersect to form a right
angle
Biconditionals
• Definition of right angle
• The midpoint of a segment is a point that
divides the segment into two congruent
segments
• Two angles are complementary if the sum of
their measures is 90 degrees
• In an equilateral polygon, all sides are
congruent