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 2. mÐ1 = mÐ2 2. Definition of an Angles Bisector I 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.

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 Statements Reasons 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

4. Given: a || b; Ð3 @ Ð4 Prove: Ð10 @ Ð1 1 2 a Statements Reasons 3 4 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 7 8 b 10 9 c d 5. Given: a || b Prove: Ð1 and Ð7 are supplementary. 1 3 b 4 5 6 7 a Statements Reasons 8 2 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

Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – Page 5 – Answer Key Date: ___________________________ 6. Given: BE bisects ÐDBA; Ð1 @ Ð3 Prove: CD // BE Statements Reasons 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

Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – page 6 – Answer Key Date: ___________________________ 7. Given: AB // CD; BC // DE Prove: Ð2 @ Ð6 Statements Reasons 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 2 6 4 1 3 5 7 A C E 8. Given: AB // CD; Ð2 @ Ð6 Prove: BC // DE Statements Reasons 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 2 6 4 1 3 5 7 A C E

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 y 5x 75° x = 21 y = 75 x = 11 5. 6. A B 4x + 13 4x + 25 5x 4x + 17 80° 83° 6x 6x D C x = 20 Is AB // DC? yes Is AD // BC? no 4x + 25 4x + 13 x = 23

Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – page 8 – Answer Key Date: ___________________________ Number of Sides Name of polygon Sum of interior angles. Measure of each interior angle if it was a regular polygon Sum of the Exterior Angles Measure of each exterior angle if it was a regular polygon. Number of Diagonals that can be drawn. 3 Triangle 180 60 360 120 4 Quadrilateral 90 2 5 Pentagon 540 108 72 6 Hexagon 720 9 7 Heptagon OR Septagon 900 128.57 51.43 14 8 Octagon 1080 135 45 20 Nonagon 1260 140 40 27 10 Decagon 1440 144 36 35 n n-gon