Unit 3 Review Packet – Answer Key

Geometry/Trig Name: __________________________ Unit 3 Review Packet – Answer Key Date: ___________________________ Section I – Name the five ways to prove that parallel lines exist. 1. If corresponding angles are congruent, then lines are parallel. 2. If alternate interior angles are congruent, then lines are parallel. 3. If alternate exterior angles are congruent, then lines are parallel. 4. If same side interior angles are supplementary, then lines are parallel. 5. If same side exterior angles are supplementary, then lines are parallel. Section II – Identify the pairs of angles. If the angles have no relationship, write none. 1. 7 & 11 None 2. 3 & 6 Alternate Interior Angles 3. 8 & 16 Corresponding Angles 4. 2 & 7 Alternate Exterior Angles 5. 3 & 5 Same Side Interior Angles 6. 1 & 6 None 7. 1 & 6 None 8. 1 & 4 Vertical Angles 1 2 3 4 a b 5 6 7 8 Section III – Fill In Vertical angles are congruent. If lines are parallel, then corresponding angles are congruent. If lines are parallel, then alternate interior angles are congruent. If lines are parallel, then alternate exterior angles are congruent. If lines are parallel, then same side interior angles are supplementary. If lines are parallel, then same side exterior angles are supplementary. 9 10 11 12 13 14 15 16 Geometry/Trig 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1 = m9 c // d 2.) m1 = m4 None 3.) m12 + m14 = 180 a // b 4.) m1 = m13 None 5.) m7 = m14 c // d 6.) m13 = m11 None 7.) m15 + m16 = 180 None 8.) m4 = m5 a //b 1 2 3 4 a b 5 6 7 8 c 9 10 11 12 13 14 15 16 d Section IV – Determine which lines, if any, are parallel based on the given information. 1. m1 = m4 a // b 2. m6 = m8 t // s 3. 1 and 11 are supplementary 4. a ^ t and b ^ t 5. m14 = m5 None a // b a None b 6. 6 and 7 are supplementary t // s 7. m14 = m15 8. 7 and 8 are supplementary 9. m5 = m10 10. m1 = m13 k // m None m 15 13 k // m k 12 11 9 8 10 None 1 2 3 4 14 5 6 t 7 s Geometry/Trig Name: __________________________ Unit 3 Review Packet – Page 3 – Answer Key Date: ___________________________ J Section V - Proofs 1. Given: GK bisects JGI; m3 = m2 G Prove: GK // HI Statements 1. GK bisects JGI 1 2 K Reasons 1. Given 3 I 2. m1 = m2 2. Definition of an Angles Bisector 3. m3 = m2 3. Given 4. m1 = m3 4. Substitution 5. GK // HI 5. If corresponding angles are congruent, then the lines are parallel. 2. Given: AJ // CK; m1 = m5 H A Prove: BD // FE C Reasons Statements 1. AJ // CK 1. Given 2. m1 = m3 2. If lines are parallel, then corresponding angles are congruent. 3. m1 = m5 3. Given 4. m3 = m5 4. Substitution 5. BD // FE 5. If corresponding angles are congruent, then the lines are parallel. 1 B F 2 4 5 J K 3 D E Geometry/Trig Name: __________________________ Unit 3 Review Packet – Page 4 – Answer Key Date: ___________________________ 3. Given: a // b; 3 @ 4 Statements 1. a // b Prove: 10 @ 1 1 a 3 5 Reasons 6 1. Given 2. 4 @ 7 2. If lines are parallel then alternate interior angles are congruent. 3. 3 @ 4 3. Given 4. 3 @ 7 4. Substitution 5. 1 @ 3; 7 @ 10 5. Vertical Angles Theorem 6. 10 @ 1 6. Substitution 4. Given: 1 and 7 are supplementary. Prove: m8 = m4 8 7 b 9 10 d c 1 b a Statements 2 4 Reasons 4 6 8 3 5 7 2 1. 1 and 7 are supplementary 1. Given 2. m1 + m7 = 180 2. Definition of Supplementary Angles 3. m6 + m7 = 180 3. Angle Addition Postulate 4. m1 + m7 = m6 + m7 4. Substitution 5. m1 = m6 5. Subtraction Property 6. a // b 6. If corresponding angles are congruent, then the lines are parallel. 7. m8 = m4 7. If lines are parallel, then corresponding angles are congruent. Geometry/Trig Name: __________________________ Unit 3 Review Packet – Page 5 – Answer Key Date: ___________________________ 5. Given: ST // QR; 1 @ 3 Prove: 2 @ 3 P Reasons Statements 1. ST // QR 1. Given 2. 1 @ 2 2. If lines are parallel, then corresponding angles are congruent. 1 S 3. 1 @ 3 3. Given 4. 2 @ 3 4. Substitution Q 3 T 2 R 6. Given: BE bisects DBA; 1 @ 3 Prove: CD // BE Reasons Statements 1. BE bisects DBA 1. Given 2. 2 @ 3 2. Definition of an Angle Bisector 3. 1 @ 3 3. Given 4. 2 @ 1 4. Substitution 5. CD // BE 5. If alternate interior angles are congruent, then the lines are parallel. C B 2 3 1 D E A Geometry/Trig Name: __________________________ Unit 3 Review Packet – page 6 – Answer Key Date: ___________________________ 7. Given: AB // CD; BC // DE Reasons Statements Prove: 2 @ 6 1. AB // CD 1. Given 2. 2 @ 4 2. If lines are parallel, then alternate interior angles are congruent. 3. BC // DE 3. Given 4. 4 @ 6 4. If lines are parallel, then alternate interior angles are congruent. 5. 2 @ 6 5. Substitution B D 6 2 A 8. 1 3 5 7 C E Given: AB // CD; 2 @ 6 Reasons Statements 4 Prove: BC // DE 1. AB // CD 1. Given 2. 2 @ 4 2. If lines are parallel, then alternate interior angles are congruent. 3. 2 @ 6 3. Given 4. 4 @ 6 4. Substitution 5. BC // DE 5. If alternate interior angles are congruent, then the lines are parallel. B D 6 2 A 1 3 4 C 5 7 E Geometry/Trig Name: __________________________ Unit 3 Review Packet – page 7– Answer Key Date: ___________________________ Section VI – Solve each Algebra Connection Problem. 1. 2. w x 4x - 5 z + 57 23y 65 37 2y w = 37 Equations: 37 = w x + 37 = 180 2y + 37 = 180 z + 57 = 143 x = 143 y = 71.5 Equations: 65 + 23y = 180 65 = 4x – 5 125 x = 17.5 y=5 z = 86 Equations: 30 + 75 = 5x 30 + 75 + y = 180 3. 30 Equation: 6x + x + 12 = 8x + 1 4. x + 12 75 y 5x 6x 8x + 1 x = 21 y = 75 x = 11 Geometry/Trig Name: __________________________ Unit 3 Review Packet – page 8 Date: ___________________________ Section VIII - Classify each triangle by its sides and by its angles. 1. 2. A D 3. G 60 B 59 F C Scalene Acute E H L 5. O M 20 I Scalene Obtuse 6. 42 55 100 Isosceles Right K 4. J 45 Q P 35 75 30 R N Scalene Right Scalene Obtuse 7. In DABC which side is the longest? AB 8. In DDEF which side is the longest? DE Isosceles Acute the shortest? AC Which two have the same length? DF = FE 9. In DGHI which side is the longest? GI the shortest? GH 10. In DJKL which side is the longest? JK the shortest? JL 11. In DMNO which side is the longest? NO the shortest? MO 12. In DPQR which side is the shortest? QR Which two have the same length? PQ = PR In each triangle, name the smallest angle and the largest angle. A 8 D 10 I 10 15 8 B C 9 E 6 F 12 G H 7 smallest