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Geometry/Trig 2 Name: __________________________

Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – Page 2 – Answer Key Date: ___________________________. Section IV – Determine which lines, if any, are parallel based on the given information. 1.) m Ð 1 = m Ð 9 c || d 2.) m Ð 1 = m Ð 4 None

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Geometry/Trig 2 Name: __________________________

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  1. Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – Page 2 – Answer Key Date: ___________________________ Section IV – Determine which lines, if any, are parallel based on the given information. 1.) mÐ1 = mÐ9 c || d 2.) mÐ1 = mÐ4 None 3.) mÐ12 + mÐ14 = 180 a || b 4.) mÐ1 = mÐ13 None 5.) mÐ7 = mÐ14 c || d 6.) mÐ13 = mÐ11 None 7.) mÐ15 + mÐ16 = 180 None 8.) mÐ4 = mÐ5 a || b 1 2 9 10 a 3 4 11 12 5 6 13 14 b 7 8 15 16 c d J Section II - Proofs 1. Given: GK bisects ÐJGI; mÐ3 = mÐ2 Prove: GK || HI 1 G K 2 Statements Reasons 1. Given 1. GK bisects ÐJGI 3 I 2. mÐ1 = mÐ2 2. Definition of an Angles Bisector H 3. mÐ3 = mÐ2 3. Given 4. mÐ1 = mÐ3; Ð1  Ð3 4. Substitution 5. GK || HI 5. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

  2. Geometry/Trig 2 Unit 3 Proofs Review – Answer Key Page 2 2. Given: AJ || CK; mÐ1 = mÐ5 Prove: BD || FE A C Reasons Statements 1 2 3 1. AJ || CK 1. Given 2. mÐ1 = mÐ3 2. If two parallel lines are Ð1 Ð3 cut by a transversal, then corresponding angles are congruent. 3. mÐ1 = mÐ5 3. Given 4. mÐ3 = mÐ5 4. Substitution Ð3 Ð5 5. BD || FE 5. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. B D 4 5 F E J K 3. Given: ST || QR; Ð1 @Ð3 Prove: Ð2 @ Ð3 P Reasons Statements • ST || QR 1. Given • 2. Ð1 @Ð2 2. If two parallel lines are cut by a transversal, then corresponding angles are congruent. • 3. Ð1 @Ð3 3. Given • 4. Ð2 @Ð3 4. Substitution 1 3 S T 2 Q R

  3. 4. Given: a || b; Ð3 @Ð4 Prove: Ð10 @Ð1 1 2 a 3 4 Statements Reasons 5 1. Ð3 @Ð4 1. Given 2. Ð1 @Ð3 2. Vertical Angles Theorem 3. Ð1 @Ð4 3. Substitution 4. a || b 4. Given 5. Ð4 @Ð7 5. If lines are parallel, then alternate interior angles are congruent. 6. Ð1 @Ð7 6. Substitution 7. Ð7 @Ð10 7. Vertical Angles Theorem 8. Ð1 @Ð10 8. Substitution 6 8 7 b 9 10 d c 5. Given: a || b Prove: Ð1 and Ð7 are supplementary. 1 3 b 4 5 6 7 a 8 2 Statements Reasons 1. a || b 1. Given 2. mÐ1 + mÐ4 = 180 2. Definition of Linear Pair/Angle Addition Postulate 3. mÐ4 = mÐ7; Ð4 Ð7 3. If lines are parallel, then alternate interior angles are congruent. 4. mÐ1 + mÐ7 = 180 4. Substitution 5. Ð1 and Ð7 are supplementary 5. Definition of supplementary angles

  4. Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – Page 5 – Answer Key Date: ___________________________ 6. Given: BE bisects ÐDBA; Ð1 @Ð3 Prove: CD // BE Reasons Statements 1. BE bisects ÐDBA 1. Given 2. Ð2 @Ð3 2. Definition of an Angle Bisector 3. Ð1 @Ð3 3. Given 4. Ð2 @Ð1 4. Substitution 5. CD // BE 5. If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. C B 2 3 1 A D E

  5. Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – page 6 – Answer Key Date: ___________________________ 7. Given: AB // CD; BC // DE Prove: Ð2 @Ð6 Reasons Statements 1. AB // CD 1. Given 2. Ð2 @Ð4 2. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. 3. BC // DE 3. Given 4. Ð4 @Ð6 4. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. 5. Ð2 @Ð6 5. Substitution B D 6 2 4 1 3 5 7 A C E 8. Given: AB // CD; Ð2 @Ð6 Prove: BC // DE Reasons Statements 1. AB // CD 1. Given 2. Ð2 @Ð4 2. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. 3. Ð2 @Ð6 5. Given 4. Ð4 @Ð6 4. Substitution 5. BC // DE 3. If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. B D 6 2 4 1 3 5 7 A C E

  6. Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – page 7– Answer Key Date: ___________________________ Section VI – Solve each Algebra Connection Problem. 1. 2. w 4x - 5 23y z + 57 x 65° 125° 37° 2y w = 37 x = 143 y = 71.5 z = 86 x = 30 y = 5 3. 4. 30° x + 12 6x 8x + 1 5x y 75° x = 21 y = 75 x = 11 5. 6. A B 4x + 25 4x + 13 5x 4x + 17 83° 80° 6x 6x D C x = 20 Is AB // DC? yes Is AD // BC? no 4x + 25 4x + 13 x = 23

  7. Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – page 8 – Answer Key Date: ___________________________

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