Geometry Chapter 2 Review Name: ______
- Logical Statements:
a. If you are 14 years old then you are a teenager.
Hypothesis:
Conclusion:
Converse:
Counterexample:
Contrapositive:
Can a true biconditional be formed in this case? If so write it. If not explain why not.
Euler Diagram:
Ben is a teenager. Deduction (if possible): / b. Odd integers are not divisible by 2.
Conditional:
Converse:
Contrapositive:
Can a true biconditional be formed in this case? If so write it. If not explain why not.
c.
Conditional:
Contrapositive:
Lindsay’s pet is a frog. Deduction (if possible):
- Logical Chain.
a) If you live in the Antarctic, you live where it is cold.
b) If you live at the South Pole, you live in the Antarctic.
c) If you need a warm coat, then you need warm socks.
d) If you live where it is cold, you need a warm coat. / This statement forms a logical chain when the statements are in this order:
______
Conditional that follows from this logical chain:
a) If the field is wet, the Pirates will not play baseball.
b) If the Pirates do not play baseball, Nathan can stop at the Scoop after school.
c) If it rains a lot, the field is wet. / This statement forms a logical chain when the statements are in this order:
______
Conditional:
a) If Kate studies well, she will get good grades.
b) If Kate lives in the dorms, she will have fun.
c) If Kate goes to college, she will live in the dorms.
d) If Kate gets good grades, she will go to college.
This statement forms a logical chain when the statements are in this order: ______
Conditional: / a) If p then w.
b) If r then y.
c) If w then r.
This statement forms a logical chain when the statements are in this order: ______
Conditional:
Does “If not y then not p” have to be true?
Why?
Inductive reasoning
Inductive reasoning is the process of arriving at a conclusion based on a set of observations. In itself, it is not a valid method of proof.
Deductive reasoning
Deductive reasoning is a valid form of proof. It is the way in which geometric proofs are written. Deductive reasoning is the process by which a person makes conclusions based on previously known facts.
In geometry, inductive reasoning can helps us organize what we observe so that we can prove theorems by using deductive reasoning.
Identify each as inductive or deductive reasoning.
a. The Pirates have won their last 3 home games. Therefore the Pirates will win their next home game. ______/ b. Angela draws 5 triangles and measures all the angles in each. She observes that the sum of the angles in each triangle is 180°. Therefore, the sum of the angles in all triangles must be 180°.
______
c. Angles that are less than 90° are acute. = 30°, therefore is acute. ______
d. Every time John eats strawberries, he breaks out in hives. Therefore John is allergic to strawberries. ______
e. If I sleep until 8 am then I am well-rested. If I am well-rested then I like to go running. Saturdays I sleep until 8 am. Therefore, I like to run on Saturdays. ______
- The following are questions from the CST geometry test. There may be questions similar to these on your test. Make sure you understand them.
a.
/ b.
c.
/ d.
e.
/ f.
- Name the definition, postulate or theorem that justifies each step. You can use your definitions, postulates and theorems handout on this question.
a. If / b. If then are complementary.
c. If then is a right angle. / d. If are vertical angles then .
e. , then / f. If , then
- For each problem a – e, fill in the correct type of angles form the list of choices. Use each answer once.
Choices: are…
Vertical Angles
A Linear Pair
Complementary and Adjacent
Complementary not Adjacent
Supplementary not Adjacent / a. / b.
c.
/ d. / e.
- Solve for x and find the measure of all angles in each diagram.
a.
/ b.
c.
/ d.
e. / f.
- Solve for x and justify each step.
Given: bisects
Prove:
- Given: are vertical;.
Prove:
You must know all of the following constructions for your test. If you need more practice create your own segments and angles and do each construction many times.
11. Perpendicular bisector of the segment. / 12. Perpendicular through point on line13. Perpendicular through point off line / 14. Angle Bisector
15. Duplicate an Angle in the box to the right. / The duplicated angle must be the same size and shape, but it does not need to orientated the same direction.
16. Duplicating Segments
Construct such that GH = AB:
Construct such that IJ = AB + 2(EF):
Construct such that KL = 2(AB) – CD: /
17. Construct the Incenter, the radius for the Incircle, and the Incircle:
18. Construct the Circumcenter and Circumcircle.
Algebra Review: The only algebra review on your test will be of the following type.
Solve: / Find the equation of the line through: Must show an algebraic method.