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Geometric Proof – HW: Biconditional Statements
1. Define biconditional statement.
2. How do you decide if a biconditional statement is true or not?
For questions 3, write all three related conditionals (converse, inverse,
contrapositive).
3. If two angles are complementary, then their sum is 90o.
For questions 4 – 6, rewrite each biconditional statement as its corresponding
conditional and its converse.
4. A variable equals one only if the variable is greater than zero.
5. It is 3:30 AM only if it is nighttime.
6. I will graduate from high school only if I pass Geometry.
For questions 7 – 8, decide if the biconditional is true or false. Show all work
needed and give a counterexample if false.
7. An angle is acute only if it measures less than 90o.
8. Three points are collinear only if they lie on the same line.
For questions 9, write the converse of the true statement. If the converse is also
true, combine the statements to write a true biconditional statement. If the
converse is false, give a counterexample.
9. If two angles are congruent, then they have the same measure.
15. If two angles are complementary, then they sum to 90o.
16. If two angles are linear pairs, then their measures add to 180o.
For questions 17 – 22, provide a counterexample to show each conjecture is false.
You may use words or a diagram.
17. If a number is divisible by 5, it is divisible by 10.
18. If a 4-sided figure has 4 right angles, then it has 4 congruent sides.
19. If a 4-sided figure has 4 congruent sides, then it has 4 right angles.
20. If line segment CD is congruent to segment DE , then D is the midpoint of
segment CE.
21. If point G is on ray AB, then G is on ray BA.
22. If ab < 0, then a < 0.