GeometryTrig Name Unit 3 Review Packet Answer Key

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Geometry/Trig Name: _____________ Unit 3 Review Packet – Answer Key Date: ______________ Section I

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. Ð 7 & Ð 11 None 2. Ð 3 & Ð 6 Alternate Interior Angles 3. Ð 8 & Ð 16 Corresponding Angles 4. Ð 2 & Ð 7 Alternate Exterior Angles 5. Ð 3 & Ð 5 Same Side Interior Angles 6. Ð 1 & Ð 16 None 7. Ð 1 & Ð 6 None 8. Ð 1 & Ð 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:

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. ) mÐ 1 = mÐ 9 c // d 2. ) mÐ 1 = mÐ 4 None 3. ) mÐ 12 + mÐ 14 = 180 a // b 4. ) mÐ 1 = mÐ 13 None 5. ) mÐ 7 = mÐ 14 c // d 6. ) mÐ 13 = mÐ 11 None 7. ) mÐ 15 + mÐ 16 = 180 None 8. ) mÐ 4 = mÐ 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. mÐ 1 = mÐ 4 a // b 2. mÐ 6 = mÐ 8 t // s 3. Ð 1 and Ð 11 are supplementary 4. a ^ t and b ^ t 5. mÐ 14 = mÐ 5 None a // b a None b 6. Ð 6 and Ð 7 are supplementary t // s 7. mÐ 14 = mÐ 15 8. Ð 7 and Ð 8 are supplementary 9. mÐ 5 = mÐ 10 10. mÐ 1 = mÐ 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:

Geometry/Trig Name: _____________ Unit 3 Review Packet – Page 3 – Answer Key Date: ______________ J Section V - Proofs 1. Given: GK bisects ÐJGI; mÐ 3 = mÐ 2 G Prove: GK // HI Statements 1 2 K Reasons 1. GK bisects ÐJGI 1. Given 2. mÐ 1 = mÐ 2 2. Definition of an Angles Bisector 3. mÐ 3 = mÐ 2 3. Given 4. mÐ 1 = mÐ 3 4. Substitution 5. GK // HI 5. If corresponding angles are congruent, then the lines are parallel. 2. Given: AJ // CK; mÐ 1 = mÐ 5 3 H Prove: BD // FE I A C Reasons Statements 1. AJ // CK 1. Given 2. mÐ 1 = mÐ 3 2. If lines are parallel, then corresponding angles are congruent. 3. mÐ 1 = mÐ 5 3. Given 4. mÐ 3 = mÐ 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:

Geometry/Trig Name: _____________ Unit 3 Review Packet – Page 4 – Answer Key Date: ______________ 3. Given: a // b; Ð 3 @ Ð 4 Statements 1. a // b Prove: Ð 10 @ Ð 1 1 a 3 5 Reasons 6 1. Given 2. Ð 4 @ Ð 7 2. If lines are parallel then alternate interior angles are congruent. 3. Ð 3 @ Ð 4 3. Given 4. Ð 3 @ Ð 7 4. Substitution 5. Ð 1 @ Ð 3; Ð 7 @ Ð 10 5. Vertical Angles Theorem 6. Ð 10 @ Ð 1 6. Substitution 4. Given: Ð 1 and Ð 7 are supplementary. Prove: mÐ 8 = mÐ 4 8 7 b 9 10 d c 1 b a Statements 2 4 Reasons 4 6 8 3 5 7 2 1. Ð 1 and Ð 7 are supplementary 1. Given 2. mÐ 1 + mÐ 7 = 180 2. Definition of Supplementary Angles 3. mÐ 6 + mÐ 7 = 180 3. Angle Addition Postulate 4. mÐ 1 + mÐ 7 = mÐ 6 + mÐ 7 4. Substitution 5. mÐ 1 = mÐ 6 5. Subtraction Property 6. a // b 6. If corresponding angles are congruent, then the lines are parallel. 7. mÐ 8 = mÐ 4 7. If lines are parallel, then corresponding angles are congruent.

Geometry/Trig Name: _____________ Unit 3 Review Packet – Page 5 – Answer Key Date:

Geometry/Trig Name: _____________ Unit 3 Review Packet – Page 5 – Answer Key Date: ______________ 5. Given: ST // QR; Ð 1 @ Ð 3 Prove: Ð 2 @ Ð 3 P Reasons Statements 1. ST // QR 1. Given 2. Ð 1 @ Ð 2 2. If lines are parallel, then corresponding angles are congruent. 1 S 3. Ð 1 @ Ð 3 3. Given 4. Ð 2 @ Ð 3 4. Substitution Q 3 T 2 R 6. Given: BE bisects ÐDBA; Ð 1 @ Ð 3 Prove: CD // BE Reasons Statements 1. BE bisects ÐDBA 1. Given 2. Ð 2 @ Ð 3 2. Definition of an Angle Bisector 3. Ð 1 @ Ð 3 3. Given 4. Ð 2 @ Ð 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:

Geometry/Trig Name: _____________ Unit 3 Review Packet – page 6 – Answer Key Date: ______________ 7. Given: AB // CD; BC // DE Reasons Statements Prove: Ð 2 @ Ð 6 1. AB // CD 1. Given 2. Ð 2 @ Ð 4 2. If lines are parallel, then alternate interior angles are congruent. 3. BC // DE 3. Given 4. Ð 4 @ Ð 6 4. If lines are parallel, then alternate interior angles are congruent. 5. Ð 2 @ Ð 6 5. Substitution B D 6 2 A 8. 1 3 5 7 C E Given: AB // CD; Ð 2 @ Ð 6 Reasons Statements 4 Prove: BC // DE 1. AB // CD 1. Given 2. Ð 2 @ Ð 4 2. If lines are parallel, then alternate interior angles are congruent. 3. Ð 2 @ Ð 6 3. Given 4. Ð 4 @ Ð 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: ______________

Geometry/Trig Name: _____________ Unit 3 Review Packet – page 7– Answer Key Date: ______________ Section VI – Solve each Algebra Connection Problem. 1. 2. w 4 x - 5 z + 57 x 23 y 65° 37° 2 y w = 37 Equations: 37 = w x + 37 = 180 2 y + 37 = 180 z + 57 = 143 x = 143 y = 71. 5 125° Equations: 65 + 23 y = 180 65 = 4 x – 5 x = 17. 5 y=5 z = 86 Equations: 30 + 75 = 5 x 30 + 75 + y = 180 3. 30° Equation: 6 x + 12 = 8 x + 1 4. x + 12 75° y 5 x 6 x 8 x + 1 x = 21 y = 75 Section VII – Determine whether the given side lengths can create a triangle. 1) 7, 8, 9 YES 2) 7, 8, 15 NO 3) 7, 8, 14 YES 4) 3, 4, 5 YES x = 11

Geometry/Trig Name: _____________ Unit 3 Review Packet – page 8 Date: ______________ Section VIII

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 104° 19 B F C K 4. E H Scalene Right Scalene Obtuse L 5. O Scalene Acute M 47 53° I Scalene Acute 6. 60° 36° J 60° Q P 60° 32° 118° R N Equilateral Equiangular 7. In DABC which side is the longest? ___BC_____ Scalene Obtuse the shortest? ______AC___ 8. In DDEF which side is the longest? _DE___ the shortest? ___EF_______ 9. In DGHI which side is the longest? ___HI_____ the shortest? _____GI____ 10. In DJKL which side is the longest? ____JK____ the shortest? ____KL_____ 11. In DMNO which side is the longest? ____all the same____ 12. In DPQR which side is the longest? _QR____ the shortest___PR_____ In each triangle, name the smallest angle and the largest angle. A D 6. 4 4. 1 I 118 12. 9 128 B C 5. 7 E Smallest <B Smallest Largest <C Largest 136 <E <D F 17. 3 G 11 Smallest Largest H <I <G