Download GPS Geometry Review for Test Rewrite the statement in if

GPS Geometry
Review for Test
Rewrite the statement in if-then form. Then write the converse of the conditional statement. If the converse is
false, provide a counterexample. If the converse is true, combine the statements to write as a bi-conditional
statement.

1. An angle that measures 37 is an acute angle.
Conditional: If an angle measures 37, then it is an acute angle
Converse: If an angle is an acute angle, then it measures 37
Is the converse true or false? False
Based on the previous answer either write a bi-conditional statement or provide a counterexample:
A 45 degree angle is an acute angle
2. Congruent angles have the same measure.
Conditional: If two angles are congruent, then they have the same measure.
Converse: If two angles have the same measure, then they are congruent.
Is the converse true or false? True
Based on the previous answer either write a bi-conditional statement or provide a counterexample:
Two angles are congruent if and only if they have the same measure.
Using p and q below, write the symbolic statement in words.
p: It is Thursday
q: Phil plays tennis
3.
p It is not Thursday
4.
q Phil does not play tennis
5.
p  q If it is Thursday, then Phil plays tennis.
6.
q  p If Phil plays tennis then it is Thursday.
7.
p  q If it is not Thursday, then Phil does not play tennis.
8.
q  p If Phil does not play tennis, then it is not Thursday.
9.
p  q It is Thursday if and only if Phil plays tennis.
Write the following statement in bi-conditional form.
10. If a figure is a quadrilateral then it has four sides.
A figure is a quadrilateral if and only if it has four sides.
Write the inverse, converse and contrapositive of the conditional statement.
11. If it is Labor Day, then it is a holiday.
Inverse: If it is not Labor Day, then it is not a holiday.
Converse: If it is a holiday, then it is Labor Day.
Contrapositive: If it is not a holiday, then it is not Labor Day.
Determine whether the argument is valid or invalid by using the Law of Detachment.
12. If a vehicle is a car, then it has four wheels.
A sedan is a car. So, a sedan has four wheels.
Valid
13. If you want a steak that is grilled to perfection then go to Morton’s.
Gail went to Morton’s. Gail wanted a steak that was grilled to perfection.
Invalid
Use the Law of Syllogism to write the statement that follows the pair of given statements.
14. If Elena takes the car to the store, then she will stop at the post office.
If Elena stops at the post office, then she will buy stamps.
If Elena takes the car to the store, then she will buy stamps.
Write a conclusion using the true statements. If no conclusion is possible, write no conclusion.
15. If I watch TV, then I will not do my homework.
I did not do my homework.
No Conclusion
16. If an angle measures less than 90 , then it is acute.
m A is less than 90
A is acute
17. If two angles form a linear pair, then they share a common ray.
If two angles share a common ray, then they are adjacent.
If two angles form a linear pair, then they are adjacent.