Geometry Test this Week in Chapter 2!

Review for Chapter 2 Test

2.1: Inductive Reasoning

2.2: If and Then Statements

2.3: Deductive Reasoning

2.6: Verifying Angle Relationships

Vocabulary

2.1

You are given a statement. Determine if the conjecture is true or false; if false, provide a counterexample.

1. G: A, B and C are not colinear. C: B is the midpoint of AC.
2. G: X, Y, Z and A are the only vertices of a polygon. C: The polygon has four sides.
3. G: Angle 1 and angle 2 form a linear pair. C: <1 180="" degrees.="" font="">

2.2

Translate the following into if - then form.

     4. The intersection of two planes is a line.

     5. Clintondale High School has a principal named Mrs. Cargill.

     6. Rick Synder is the governor of Michigan.

Rewrite each aforementioned sentence into the specified conditional statement.

    7. (Contrapositive) ___________________________________________________________________________

    8. (Inverse) ___________________________________________________________________________

    9. (Converse)

___________________________________________________________________________

2.3

Use the Law of Detachment to determine if the statements are valid,invalid or fill in the blank to make valid.

     10. If a person is a celebrity, then that person is famous.

          Justin Bieber is a celebrity. Justin Escalante is famous.

    11. If a car has gas in the tank, then that car will emit carbon emissions.

         A Volkswagon has gas in the tank. The Volkswagon will emit carbon emissions.

    12. If the president of the neighborhood association is a veteran, then that person can go to the      VA hospital for treatment. President Scarsdale of Pickney Neighborhood served in Iraq. ______________________________________________________________________________

Use the Law of Syllogism to determine if the statements are invalid or fill in the blank to make valid.

    13. The sun is a star. Stars are in constant motion. ______________________________________________________________________________

    14. The principal of CMS is Ira Hamden. The vice principal of CMS is Tim Baldwin. ______________________________________________________________________________

    15. Cops were academy trainees. Trainees had to endure physical endurance. ______________________________________________________________________________

    16. “Supermoon” was a spectacular event. Spectacular events are apart of recorded history. ______________________________________________________________________________

    17. CHS has many organizations for students. There are many organizations is public schools. ______________________________________________________________________________

2.6

For each statement, it is always true, sometimes true, or never true.

18. Two angles that are congruent are ________ complementary to the same angle.

19. Two angles that are vertical are _________ nonadjacent.

20. Two angles that form a right angle are __________ complementary.

21. Vertical angles are ________ supplementary.

22. Angles with a common side and a common vertex __________ form a linear pair.

*Looking at the above picture, if angle one equals angle two, what can you say about the sum of angle two and angle three?