Name: ________________________ Class: ___________________ Date: __________
Chapter 2 Study Guide Find the next item in each pattern. 1.
2. 405, 135, 45, 15, ...
Complete the conjecture 3. The sum of an even number and an odd number is ___________ 4. The square of a natural number is ____________.
Determine if each conjecture is true. If not, write or draw a counterexample. 5. All complementary angles are adjacent. 6. If C is the midpoint of AB, then AC ≅ CB. 7. If two lines intersect, then they form four right angles. 8. Use the Venn diagram to write a conditional statement.
9. Write the inverse, converse, and contrapositive of the conditional statement. If m∠1 = 35°, then ∠1 is acute.
Inverse
Converse
Contrapositive
1
ID: A
Name: ________________________
ID: A
Use the true statements below to determine whether each conclusion is true or false. Sue is a member of the swim team. When the team practices, Sue swims. The team begins practice when the pool opens. The pool opens at 8 A.M. on weekdays and at 12 noon on Saturday. 10. The swim team practices on weekdays only. 11. Sue swims on Saturdays. 12. Swim team practice starts at the same time every day. 13. Use the Law of Syllogism to draw a conclusion from the given information.
Given: If a figure is a square, then it is a quadrialteral. If a figure is a quadrilateral, then it is a polygon. Figure ABCD is a square. 14. Determine if the following conjecture is valid by the Law of Detachment.
Given: It it is colder than 50°F, Tom wears a sweater. It is 46°F today. Conjecture: Tom is wearing a sweater. 15. Given: 8 − 5s = 1 1 Prove: s = 5
Statements
Reasons
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Name: ________________________
ID: A
16. Given: 5x − 3 = 4(x + 2) Prove: x = 11
Statements
Reasons
17. Fill in the blanks to complete the two-column proof. Given: ∠1 and ∠2 are supplementary. m∠1 = 135°
Prove: m∠2 = 45° Proof: Statements 1. ∠1 and ∠2 are supplementary. 2. [1] 3. m∠1 + m∠2 = 180° 4. 135° + m∠2 = 180° 5. m∠2 = 45°
Reasons 1. Given 2. Given 3. [2] 4. Substitution Property 5. [3]
3
ID: A
Chapter 2 Study Guide Answer Section 1. 2. 3. 4. 5.
5 odd positive False
6. True 7. False
8. If it is Monday, then it is a weekday. 9. Converse: If ∠1 is acute, then m ∠1 = 35°. Not all acute angles measure 35°, so this is false. Inverse: If m ∠1 ≠ 35°, then 1 is not acute. You can draw an acute angle that does not measure 35°, so this is false. Contrapositive: If ∠1 is not acute, then m ∠1 ≠ 35°. An angle that measures 35° must be acute. So this statement is true.
10. 11. 12. 13. 14. 15.
False True False
Figure ABCD is a polygon. Valid Statements 8 − 5s = 1 −5s = −1 1 s= 5
Reasons Given Subtraction Prop. Division prop.
1
ID: A 16. Statements 5x − 3 = 4(x + 2) 5x − 3 = 4x + 8 x−3= 8 x = 11
Reasons Given Distributive Prop. Subtraction prop. Addition prop.
17. [1] m∠1 = 135° [2] Definition of supplementary angles [3] Subtraction Property of Equality
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