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. Ð7 & Ð11 None 2. Ð3 & Ð6 Alternate Interior Angles 3. Ð8 & Ð16 Corresponding Angles 4. Ð2 & Ð7 Alternate Exterior Angles 5. Ð3 & Ð5 Same Side Interior Angles 6. Ð1 & Ð16 None 7. Ð1 & Ð6 None 8. Ð1 & Ð4 Vertical Angles 1 2 9 10 a 3 4 11 12 5 6 13 14 b 7 8 15 16 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.

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.) 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 Section IV – Determine which lines, if any, are parallel based on the given information. 1. mÐ1 = mÐ4 a // b 2. mÐ6 = mÐ8 t // s 3. Ð1 and Ð11 are supplementary None 4. a ^ t and b ^ t a // b 5. mÐ14 = mÐ5 None 6. Ð6 and Ð7 are supplementary t // s 7. mÐ14 = mÐ15 k // m 8. Ð7 and Ð8 are supplementary None 9. mÐ5 = mÐ10 k // m 10. mÐ1 = mÐ13 None a b k m 15 t 13 12 11 9 8 7 10 2 5 1 3 4 6 s 14

Geometry/Trig Name: __________________________ Unit 3 Review Packet – Page 3 – Answer Key Date: ___________________________ J Section V - 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 4. Substitution 5. GK // HI 5. If corresponding angles are congruent, then the lines are parallel. 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 lines are parallel, then corresponding angles are congruent. 3. mÐ1 = mÐ5 3. Given 4. mÐ3 = mÐ5 4. Substitution 5. BD // FE 5. If corresponding angles are congruent, then the lines are parallel. B D 4 5 F E J K

Geometry/Trig Name: __________________________ Unit 3 Review Packet – Page 4 – Answer Key Date: ___________________________ 3. Given: a // b; Ð3 @ Ð4 Prove: Ð10 @ Ð1 1 2 a 3 4 Statements Reasons 5 6 1. a // b 1. Given 2. Ð4 @ Ð7 2. If lines are parallel then alternate interior angles are congruent. 3. Ð3 @ Ð4 3. Given 4. Ð3 @ Ð7 4. Substitution 5. Ð1 @ Ð3; Ð7 @ Ð10 5. Vertical Angles Theorem 6. Ð10 @ Ð1 6. Substitution 7 8 b 10 9 c d 4. Given: Ð1 and Ð7 are supplementary. Prove: mÐ8 = mÐ4 1 3 b 4 5 6 7 a Statements Reasons 8 2 1. Ð1 and Ð7 are supplementary 1. Given 2. mÐ1 + mÐ7 = 180 2. Definition of Supplementary Angles 3. mÐ6 + mÐ7 = 180 3. Angle Addition Postulate 4. mÐ1 + mÐ7 = mÐ6 + mÐ7 4. Substitution 5. mÐ1 = mÐ6 5. Subtraction Property 6. a // b 6. If corresponding angles are congruent, then the lines are parallel. 7. mÐ8 = mÐ4 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; Ð1 @ Ð3 Prove: Ð2 @ Ð3 P Statements Reasons ST // QR 1. Given 2. Ð1 @ Ð2 2. If lines are parallel, then corresponding angles are congruent. 3. Ð1 @ Ð3 3. Given 4. Ð2 @ Ð3 4. Substitution 1 3 S T 2 Q R 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 alternate interior angles are congruent, then the lines are parallel. C B 2 3 1 A D E

Geometry/Trig 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 lines are parallel, then alternate interior angles are congruent. 3. BC // DE 3. Given 4. Ð4 @ Ð6 4. If lines are parallel, 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 lines are parallel, then alternate interior angles are congruent. 3. Ð2 @ Ð6 3. Given 4. Ð4 @ Ð6 4. Substitution 5. BC // DE 5. If alternate interior angles are congruent, then the lines are parallel. B D 2 6 4 1 3 5 7 A C E

Geometry/Trig 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 Equations: 37 = w x + 37 = 180 2y + 37 = 180 z + 57 = 143 w = 37 x = 143 y = 71.5 z = 86 Equations: 65 + 23y = 180 65 = 4x – 5 x = 17.5 y = 5 Equations: 30 + 75 = 5x 30 + 75 + y = 180 Equation: 6x + x + 12 = 8x + 1 3. 4. 30° x + 12 y 5x 75° 6x 8x + 1 x = 21 y = 75 x = 11 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

Equilateral Equiangular Scalene Obtuse Geometry/Trig Name: __________________________ Unit 3 Review Packet – page 8 Date: ___________________________ Section VIII - Classify each triangle by its sides and by its angles. 1. A 2. D 3. G 104° 47 53° 19 60° E F H B C I Scalene Right Scalene Obtuse Scalene Acute 4. K 5. O 6. Q 60° 32° P 118° 36° J M 60° L N R Scalene Acute Equilateral Equiangular Scalene Obtuse 7. In DABC which side is the longest? ___BC_____ 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 I 6.4 4.1 118 12.9 128 17.3 C F G B 5.7 E 136 11 H Smallest <B Smallest <E Smallest <I Largest <C Largest <D Largest <G