Download Day 4 Notes Biconditional Statements

Day 4 Notes Biconditional Statements
PreAP Geometry
Notes 2­3 Biconditional Statements
Name________________________
Date_____________Per_________
A valid biconditional statement can be formed only if a conditional statement and its converse are both true. Then you can write them as a single biconditional statement.
True conditional: If a shape is a triangle, then it has exactly three sides.
*
True converse: If a shape has exactly three sides, then it is a triangle.
Resulting BICONDITIONAL:
*
A shape is a triangle if and only if it has exactly three sides.
A shape is a triangle iff it has exactly three sides.
biconditional: double arrow
p q
If p, then q and if q, then p.
Examples: Write each biconditional as a conditional and its converse. Then determine whether the biconditional is true or false. If false, give a counterexample.
1. An angle is a right angle if and only if its measure is 90.
* True
* If an angle is right, then the angle measures 90. Conditional: ______________________________________________.
* If an angle measures 90, then the angle is right.
Converse: _______________________________________________.
2. x > ­2 iff x is positive. * False
* Let x = ­1. Then ­1 > ­2, but ­1 is not positive.
* If x > ­2, then x is positive.
Conditional: ______________________________________________.
* If x is positive, then x > ­2.
Converse: _______________________________________________.
For each conditional, write the converse and a biconditional statement.
3. Conditional: If the date is July 4th, then it is Independence Day.
* If it is Independence Day, then it is July 4th.
Converse: _________________________________________.
* It is July 4th iff it is Independence Day.
Biconditional: _________________________________________.
.
4. Conditional: If two angles are congruent, then their measures are equal.
* If two angles measures are equal, then the angles are congruent.
Converse: _________________________________________. * Two angles are congruent iff their measures are equal.
Biconditional: _________________________________________.
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Day 4 Notes Biconditional Statements
Practice
* converse
1. A biconditional statement combines a conditional and its ____________.
2. A biconditional statement can be written in the form "p if and only if q," which means * q p
"if p, then q, and if ______, then _______."
Write the converse from the given biconditional.
3. Biconditional: A figure is a segment iff it is straight and has two endpoints.
Conditional: If a figure is a segment, then it is straight and has two endpoints.
* If a figure is straight and has two endpoints, then it is a segment.
Converse: __________________________________________.
Write a converse and a biconditional from the given conditional.
4. Conditional: If two angles share a side, then they are adjacent.
* If two angles are adjacent, then they share a side.
Converse: ____________________________________________________.
* Two angles are adjacent iff they share a side.
Biconditional: __________________________________________________.
Write each biconditional as a conditional and its converse. Then determine whether the biconditional is true or false. If false, give a counterexample.
5. The tea kettle is whistling if and only if the water is boiling. T or F
* If the tea kettle is whistling, then the water is boiling. True
Conditional: __________________________________________________.
* If the water is boiling, then the tea kettle is whistling. False
Converse: ___________________________________________________.
* Counterexample: Water is boiling in a pot or in the water boiler.
6. Two angles are complementary iff they form a right angle. T or F
* If two angles are complemetary, then they form a right angle. False
Conditional: __________________________________________________.
* If two angles form a right angle, then they are complementary. True
Converse: ___________________________________________________.
* Counterexample: Two
7. <1 and <2 are vertical angles iff they are congruent. T or F
* If <1 and <2 are vertical angles, then they are congruent. True
Conditional: _________________________________________________.
* If <1 and < 2 are congurent, then they are vertical angles. False
Converse: ___________________________________________________.
* Counterexample: Two angles are separated.
8. Three points lie on the same line iff they are collinear. T or F
* If three points lie on the same line, then they are collinear. True
Conditional: __________________________________________________.
* If three points are collinear, then they are lie on the same line. True.
Converse: ___________________________________________________.
Some figures that are piggles are shown below, as are some nonpiggles.
* If it is a piggle, then it closes and does not cross.
9. Definition of piggle: ________________________________________________.
Tell whether each of the following is a piggle.
10.
11.
12.
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