Download Geometry Corrective Exercise: Identifying Patterns and Proving Statements and more Study notes Geometry in PDF only on Docsity!
Name: ________________________ Class: ___________________ Date: __________ ID: A
Geometry - Chapter 2 Corrective 1
Multiple Choice Identify the choice that best completes the statement or answers the question.
____ 1. Make a table of values for the rule x^2 ā 16 x + 64 when x is an integer from 1 to 6. Make a conjecture about the type of number generated by the rule. Continue your table. What value of x generates a counterexample? a. The pattern appears to be an decreasing set of perfect squares. x = 9 generates a counterexample. b. The pattern appears to be a decreasing set of prime numbers. x = 8 generates a counterexample. c. The pattern appears to be a decreasing set of perfect squares. x = 7 generates a counterexample. d. The pattern appears to be an increasing set of perfect squares. x = 8 generates a counterexample.
____ 2. Write the definition as a biconditional. An acute angle is an angle whose measure is less than 90 Ā°. a. An angle is acute if its measure is less than 90 Ā°. b. An angle is acute if and only if its measure is less than 90 Ā°. c. An angleās measure is less than 90 Ā° if it is acute. d. An angle is acute if and only if it is not obtuse.
____ 3. Write a justification for each step.
mā JKL = 100 Ā°
mā JKL = mā JKM + mā MKL [1] 100 Ā° = ( 6 x + 8 )Ā° + ( 2 x ā 4 )Ā° Substitution Property of Equality 100 = 8 x + 4 Simplify. 96 = 8 x Subtraction Property of Equality 12 = x (^) [2] x = (^12) Symmetric Property of Equality
a. [1] Transitive Property of Equality [2] Division Property of Equality b. [1] Angle Addition Postulate [2] Division Property of Equality c. [1] Angle Addition Postulate [2] Simplify. d. [1] Segment Addition Postulate [2] Multiplication Property of Equality
Name: ________________________ ID: A
____ 4. There is a myth that a duckās quack does not echo. A group of scientists observed a duck in a special room, and they found that the quack does echo. Therefore, the myth is false. Is the conclusion a result of inductive or deductive reasoning? a. Since the conclusion is based on a pattern of observation, it is a result of inductive reasoning. b. Since the conclusion is based on a pattern of observation, it is a result of deductive reasoning. c. Since the conclusion is based on logical reasoning from scientific research, it is a result of inductive reasoning. d. Since the conclusion is based on logical reasoning from scientific research, it is a result of deductive reasoning.
____ 5. Fill in the blanks to complete the two-column proof. Given : ā 1 and ā 2 are supplementary. mā 1 = 135Ā°
Prove : mā 2 = 45Ā°
Proof : Statements Reasons
- ā 1 and ā 2 are supplementary. 1. Given
- [1] 2. Given
- mā 1 + mā 2 = 180Ā° 3. [2]
- 135Ā° + mā 2 = 180Ā° 4. Substitution Property
- mā 2 = 45Ā° 5. [3]
a. [1] mā 2 = 135Ā° [2] Definition of supplementary angles [3] Subtraction Property of Equality b. [1] mā 1 = 135Ā° [2] Definition of supplementary angles [3] Substitution Property c. [1] mā 1 = 135Ā° [2] Definition of supplementary angles [3] Subtraction Property of Equality d. [1] mā 1 = 135Ā° [2] Definition of complementary angles [3] Subtraction Property of Equality
Name: ________________________ ID: A
Match each vocabulary term with its definition. a. conclusion b. converse c. inverse d. negation e. hypothesis f. truth value g. contrapositive
____ 19. the statement formed by both exchanging and negating the hypothesis and conclusion
____ 20. the contradiction of a statement by using ānot,ā written as ā¼
____ 21. the statement formed by exchanging the hypothesis and conclusion of a conditional statement
____ 22. operations that undo each other
____ 23. for a statement, either true ( T ) or false ( F )
Match each vocabulary term with its definition. a. deductive reasoning b. paragraph proof c. proof d. theorem e. inductive reasoning f. two-column proof g. flowchart proof
____ 24. a style of proof in which the statements are written in the left-hand column and the reasons are written in the right-hand column
____ 25. a style of proof that uses boxes and arrows to show the structure of the proof
____ 26. a style of proof in which the statements and reasons are presented in paragraph form
____ 27. a statement that has been proven
____ 28. an argument that uses logic to show that a conclusion is true
Name: ________________________ ID: A
Short Answer
- Write a justification for each step, given that EG = FH.
EG = FH Given information EG = EF + FG [1] FH = FG + GH Segment Addition Postulate EF + FG = FG + GH [2] EF = GH Subtraction Property of Equality
- Write a conditional statement from the statement. A horse has 4 legs.
ID: A
SHORT ANSWER
29. ANS:
[1] Segment Addition Postulate [2] Substitution Property of Equality
TOP: 2-6 Geometric Proof
- ANS: If it is a horse then it has 4 legs.
TOP: 2-2 Conditional Statements
