67. Which reason and statement are missing from the following proof? B C. Given

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1 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page 1 Dr. Kevin Kiyoi Geometry 10, Per 4 Amador Vaey Form Number Practice Geo Objectives: (5 of 5 isted) 31. Proofs: Agebra & properties of equaity 32. Proofs: Ange & segment addition 33. Proofs: Anges 34. Proofs: Trianges 35. Proofs: Parae ines 66. Identify the correct concusion based on the given information: : 1 and 2 are compementary anges. 1 and 3 are compementary anges. [A] 2 3 [B] 1 3 [C] 1 2 [D] 2 and 3 are compementary anges. 67. Which reason and statement are missing from the foowing proof : n m and n AB DE Prove: ABC EDC A B C m D n E n m and n AB DE ABC and EDC are right anges. ABC and EDC are right trianges. Definition of right triange. Vertica anges are congruent. ABC EDC LA right triange congruence theorem [A] A right anges are congruent.; BAC DEC [B] Perpendicuar ines form right anges.; ACB ECD [C] Vertica anges are congruent.; ACD ECB [D] Definition of right ange.; ACB ECD

2 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page What is the missing reason in the proof beow : m M = 62, m O= 54 Prove: m N =64 N M O 1. m M = 62, m O= m M + m N + m O= m N+ 54 = Substitution property 4. m N = Subtraction property of equaity [A] Ange Addition Postuate [B] If two ange are suppementary to the same ange, they are congruent to each other. [C] The sum of the s in a is 180. [D] Addition property of equaity 69. : 3 5 Prove: a b a b What reason woud be given for step 2 in the proof beow ab 2. [A] If two ines are cut by a transversa so that corresponding s are, then the ines are. [B] If two ines are cut by a transversa so that interior s are, then the ines are. [C] If two ines are cut by a transversa so that aternate interior s are, then the ines are. [D] If two ines are cut by a transversa so that suppementary s are, then the ines are. 70. Which statement is an exampe of the mutipication property [A] If x 4= 6, then x 4+ 4= [B] If x = 3, then x+ 5= [C] If 2 = 7, then ( ) = ( ) x x 2 7 [D] If x = 5, then 5 = x.

3 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page Suppy the missing reason and statement in the two-coumn proof: Consider m AFD = m 5and m EFB = m 6 : m 5= m 6 B C Prove: m 1= m 4 A D F E m 5= m 6 m 1 + m BFD = m 5, m 4 + m BFD = m 6 Ange addition property m 1= m 5 m BFD, m 4= m 6 m BFD Subtraction property of equaity m 1= m 4 Substitution [A] Subtraction property of equaity; m 5 m BFD = m 6 m BFD [B] Addition property of equaity; m 5+ m BFD = m 6+ m BFD [C] Transitive property; m 5 m BFD = m 6 m BFD [D] Transitive property; m 5+ m BFD = m 6+ m BFD 72. : 2 is suppementary to 5 Prove: a b [A] If two ines are cut by a transversa transversa are supp., then the ine a b What reason woud be given for step 2 in the proof beow 1. 2 is suppementary to ab 2.

4 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page Which two-coumn proof is correct : 2 and 5 are suppementary Prove: m m [A] 2 and 5 are supp. 2 3 Vertica Anges 7 and 4 are supp. Substitution m Same - side Interior Anges Converse [B] 2 and 5 are supp. 2 3 Aternate Exterior Anges 3 and 5 are supp. Aternate Exterior Anges m Same - side Interior Anges Converse [C] 2 and 5 are supp. 2 3 Vertica Anges 3 and 5 are supp. Substitution m Same - side Interior Anges Converse [D] none of these 74. In the foowing proof, which is the reason for the ast step 1and 2 are a inear pair 1and 2 are suppementary [A] Vertica anges are congruent. [B] Anges suppementary to the same ange or to congruent anges are congruent. [C] Linear pair postuate [D] Anges compementary to the same ange or to congruent anges are congruent.

5 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page Identify the property which justifies the foowing concusion: : 5e+ 30f Concusion: 5 e+ 6f [A] division property [C] distributive property [B] transitive property [D] substitution property b g 76. Suppy the missing reason and statement in the two-coumn proof: : Prove: AC = BD AB = CD A B C D E 1. AC = BD AC BC = BD BC 2. Addition property of equaity 3. AB + BC = AC, BC + CD = BD Addition property 5. AB = CD 5. Substitution [A] Substitution; AB = AC BC, CD = BD BC [B] Segment addition property; CD = DE, AB = DE [C] Segment addition property; AB = AC BC, CD = BD BC [D] Substitution; CD = DE, AB = DE 77. Identify the property which justifies the foowing concusion: : t = u and u= v Concusion: t = v [A] addition property [C] distributive property [B] symmetric property [D] transitive property

6 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page Compete the missing step of the foowing proof: : x+ 9= 15; 15= y 10; z+ 10= y Prove: x = z 9 x+ 9= 15; 15= y 10; z+ 10= y x+ 9= y 10 z = y 10 x + 9 = z Transitive property of equaity Addition property of equaity Transitive property of equaity [A] x = z 9; Distributive property [B] x = z 9; Transitive property of equaity [C] x = z 9; Refexive property of equaity [D] x = z 9; Addition property of equaity 79. Identify the correct concusion based on the given information: : Point B is between points A and C. Point D is between points B and C. [A] Point Dis between points A and B. [B] Point Dis between points A and C. [C] Point Bis the midpoint of AC. [D] Point Dis the midpoint of BC.

7 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page Which reason and statement are missing from the foowing proof : BCY AD B BC AD E Prove: Eis the midpoint of BD C BC YY AD BC AD A D ABCD is a paraeogram The diagonas of a paraeogram bisect each other. Eis the midpoint of BD Definition of bisect [A] Opposite sides are parae.; AE [C] A pair of opposite sides are parae and congruent.; BE = ED [D] Aternate interior anges are congruent.; AE = EC 81. Compete the missing step of the foowing proof: : x 12 = 5; 5 = y+ 11; z 11 = y Prove: x = z+ 12 x 12 = 5; 5 = y+ 11; z 11 = y x 12 = y+ 11 z = y+ 11 x = z+ 12 [A] x 12 = z 11; Transitive property of equaity [B] x 12 = z 11; Addition property of equaity = EC [B] Opposite sides are congruent.; BE = ED Transitive property of equaity Addition property of equaity Addition property of equaity [C] x 12 = z; Addition property of equaity [D] x 12 = z; Transitive property of equaity

8 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page Suppy the missing reason and statement in the two-coumn proof: Consider m AFC = m 5and m EFC = m 6 : m 5= m 6, m 2= m 3 B C Prove: m 1= m 4 A D F E m 5= m 6, m 2= m 3 m 1+ m 2= m 5, m 3+ m 4= m 6 Ange addition property m 1+ m 2= m 3+ m 4 Substitution property m 1= m 4 Addition property of equaity [A] Refexive property; m 1+ m 2= m 2+ m 4 [B] Refexive property; m 1 m 2= m 2 m 4 [C] Substitution property; m 1 m 2= m 2 m 4 [D] Substitution property; m 1+ m 2= m 2+ m Which statement is the missing reason from the proof 1and 2 are vertica anges 1 2 [A] Anges suppementary to the same ange or to congruent anges are congruent. [B] Suppement Theorem [C] Anges compementary to the same ange or to congruent anges are congruent. [D] Vertica anges are congruent.

9 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page What is the missing reason in the proof beow : m J = 58, m K = 60 Prove: m L=62 K J L 1. m J = 58, m K = m J + m K + m L= The sum of the s in a is m L= m L= Subtraction property of equaity [A] Addition property of equaity [B] Substitution property [C] Ange Addition Postuate [D] If two ange are suppementary to the same ange, they are congruent to each other. 85. Which statement is the missing reason from the proof 1and 2 are a inear pair 1and 2 are suppementary Linear pair postuate m 1 + m 2= 180 [A] Definition of suppementary [B] Vertica anges are congruent. [C] Anges suppementary to the same ange or to congruent anges are congruent. [D] Anges compementary to the same ange or to congruent anges are congruent.

10 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page Which two-coumn proof is correct : 8 and 3 are suppementary Prove: m m [A] 8 and 3 are supp. 8 5 Vertica Anges 5 and 3 are supp. Substitution m Same - side Interior Anges Converse [B] 8 and 3 are supp. 8 5 Aternate Exterior Anges 5 and 3 are supp. Aternate Exterior Anges m Same - side Interior Anges Converse [C] 8 and 3 are supp. 8 5 Vertica Anges 7 and 1 are supp. Substitution m Same - side Interior Anges Converse [D] none of these

11 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page Suppy the missing reason and statement in the two-coumn proof: : AC = CE, AB = DE Prove: BC = CD A B C D E 1. AC = CE, AB = DE AC AB = CE AB 2. Addition property of equaity 3. AC AB = CE DE Segment addition property 5. BC = AC AB, CD = CE DE 5. Addition property of equaity 6. BC = CD 6. Substitution [A] Associative property; AB + BC = AC, CD + DE = CE [B] Substitution; AB + BC = AC, CD + DE = CE [C] Associative property; AB + BC = CE, CD + DE = AC [D] Substitution; AB + BC = CE, CD + DE = AC

12 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page Which proof is correct : Y m Prove: 1 and 6 are suppementary [A] [B] [C] Y m 1 4 Vertica anges 4 and 6 are supp. Same-side interior anges 1and 6 are supp. Substitution Y m 1 4 Vertica anges 3 and 6 are supp. Same-side interior anges 1and 6 are supp. Substitution Y m 1 4 Same-side interior anges 4 and 6 are supp. Vertica anges 1and 6 are supp. Substitution [D] none of these

13 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page Pace the ettered steps from the two-coumn proof in the correct numbered steps: C D : DC DB, AB AE Prove: DC Y AE B A E 1. DC DB, AB AE DC AE 5. Converse of at. interior anges theorem YY (a) C E Substitution property (b) DBC ABE Vertica ange theorem (c) C DBC, E ABE Isoscees triange theorem [A] 2. (c) 3. (a) 4. (b) [B] 2. (a) 3. (b) 4. (c) [C] 2. (a) 3. (c) 4. (b) [D] 2. (c) 3. (b) 4. (a)

14 Acceerated Math : Wednesday, January 11, 2006, 9:49:53 AM Page Suppy the missing reason and statement in the two-coumn proof: Consider m AFC = m 5and m DFB = m 6 : m 1= m 3 B C Prove: m 5 = m 6 A D F E m 1= m 3 m 1+ m 2 = m 3 + m 2 Addition property of equaity m 1+ m 2= m 5, m 3+ m 2= m 6 Substitution [A] Ange addition property; m 1+ m 2 = m 3 + m 4 [B] Substitution; m 5 = m 6 [C] Ange addition property; m 5 = m 6 [D] Substitution; m 1+ m 2 = m 3 + m 4 End of Assignment

Test Review: Geometry I Period 1,3 Test Date: Tuesday November 24

Test Review: Geometry I Period 1,3 Test Date: Tuesday November 24 Test Review: Geoetr I Period 1,3 Test Date: Tuesda Noveber 24 Things it woud be a good idea to know: 1) A ters and definitions (Parae Lines, Skew Lines, Parae Lines, Perpendicuar Lines, Transversa, aternate