GEOMETRY CHAPTER 2 REVIEW / PRACTICE TEST
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1 GEOMETRY CHAPTER 2 REVIEW / PRACTICE TEST Name: Date: Hour: SECTION 1: Rewrite the conditional statement in If-Then Form. Then write its Converse, Inverse, and Contrapositive. 1) Adjacent angles share a common side. IF-THEN: CONVERSE: INVERSE: CONTRAPOSITIVE: SECTION 2: Rewrite the definition as a biconditional statement. 2) If two lines are perpendicular, then they intersect to form four right angles. SECTION 3: Use the diagram and the definitions you have learned so far to explain whether or not each statement is true. Explain your reasoning. 3) m XYV = 90 4) YW is the angle bisector of VYZ 5) XYU and UYZ are a linear pair. 6) XYU ZYW
2 SECTION 4: State what each symbol means for conditional statements. 7) p 8) q 9) ~ 10) 11) p q 12) q p 13) ~p ~q 14) ~q ~p SECTION 5: Create a truth table for each statement. 15) ~p ~q 16) ~(q ~p) SECTION 6: Predict the next three numbers in the sequence. 17) 3, 5, 9, 15, 23,,, 18) 7, -14, 28, -56,,, 19) 0.1, 1.2, 2.3, 3.4,,, 20) 1, 2, 3, 5, 7, 11, 13,,, 21) #20 is a special series of numbers. 1 point extra credit if you know its name! SECTION 7: Sketch the next shape in the pattern. 22) 23) SECTION 8: Show the statement is false by providing a counterexample. 24) Every triangle has at least one line of symmetry. (Sketch the counterexample) SECTION 9: Write a conjecture about the pattern described. 25) A cube with side length 2 ft has a volume of 8 ft 3. CONJECTURE: A cube with side length 3 ft has a volume of 27 ft 3. A cube with side length 4 ft has a volume of 64 ft 3. A cube with side length 5 ft has a volume of 125 ft 3.
3 SECTION 10: Decide if deductive or inductive reasoning is shown. 26) Kara knows that the Homecoming dress at Maurice s costs less than the dress at Dillard's. She also knows that the dress at Dillard's costs less than the dress at Macy s. So she reasons that the dress at Maurice s must cost less than the dress at Macy s. 27) Eva knows that that the Homecoming dress at JC Penny costs more than the dress at Kohl s. All the other dresses she has seen have cost less than the dress at JC Penny, so she reasons that the dresses at Charlotte Russe will cost less than the dress at JC Penny. SECTION 11: Determine whether or not the argument is valid based on the Law of Detachment. 28) If an angle is acute, then it is not obtuse. A is not obtuse. Therefore, A is acute. 29) If a point is the midpoint of a segment, then it divides it into two congruent segments. Q is the midpoint of line segment PR. Therefore, PQ = QR. SECTION 12: Use the Law of Syllogism to write the statement that follows from the pair of true statements. 30) If you wear orange and black, then you have school spirit. If you have school spirit, then the team feels great. 31) If two angles form a linear pair, then the sum of their measures is 180. If the sum of the measures of two angles is 180, then the angles are supplementary. SECTION 13: State the postulate that verifies the truth of the statement. 32) Lines m and l intersect at point Q. 33) Points P, Q, and S lie on plane A. 34) Line l contains points Q and R. 35) Planes A and C intersect at line l. 36) Points P and Q lie on line m. 37) Plane C contains points Q, R, and T. 38) Points Q and R lie on plane C, therefore line l lies on plane C as well.
4 SECTION 14: Find the measure of each angle given that m WPV = 38 and m QPR = m SPU = ) m RPS = 40) m QPV = 41) m QPW = 42) m SPT = 43) m TPU = 44) m WPT = SECTION 15: Draw the diagram described. State which angles are congruent. 45) ABC and CBD are complementary, adjacent angles. EBC and CBD are supplementary, adjacent angles. EBF and CBD are vertical angles. CONGRUENT ANGLES: SECTION 16: Use the given properties to complete each statement. 46) Multiplication Property of Equality: If (m A) = 22, then m A = 47) Subtraction Property of Equality: If PQ TU = RS TU, then 48) Substitution property of Equality: If FG + GH = 20 and GH = 9, then 49) Reflexive Property of Equality: For any line segment XY, XY = 50) Transitive Property of Equality: If m A = m B and m B = m C, then m A = 51) Symmetric Property of Equality: If UV = WX, then 52) Addition Property of Equality: If AB + EF = CD + EF, then 53) Division Property of Equality: If 4(m K) = 56, then m K = SECTION 17: Write an algebraic proof to solve the equation. 54) 1) 19x + 45 = 8(3x 5) 1) 2) 2) 3) 3) 4) 4) 5) 5)
5 SECTION 18: Write a two-column proof. 55) GIVEN: WX = 30, WX XY, XY YZ PROVE: YZ = 30 56) GIVEN: JM JK and KL JK, K L PROVE: J L 57) GIVEN: 1 4 PROVE: 2 3
6 58) GIVEN: RQT QRT PROVE: PQT SRT 59) GIVEN: m PMQ = 74 PROVE: m PMN = 43 and m NMQ = 31 SECTION 19: Rewrite the proof of your choice from Section 18 as a paragraph proof. 60)
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