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                        1  2     9 10
  3. 8 &16       Corresponding Angles                     a      3 4      11 12
  4. 2 &7        Alternate Exterior Angles
  5. 3 &5        Same Side Interior Angles              b      5 6     13 14
                                                                7   8    15 16
  6. 1 & 6      None
  7. 1 & 6       None
  8. 1 & 4       Vertical Angles
  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.) m1 = m9            c // d                                 a       1  2     9 10
  2.) m1 = m4            None                                          3 4      11 12
  3.) m12 + m14 = 180    a // b                               b      5 6     13 14
                                                                      7   8    15 16
  4.) m1 = m13           None                                      c        d
  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
  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     None
  4. a ^ t and b ^ t     a // b
  5. m14 = m5      None                                     a          b      k
                                                                                          m
  6. 6 and 7 are supplementary   t // s                                 15
  7. m14 = m15     k // m                                 13  12   11   9      8          t
                                                                                     7
                                                                       10
  8. 7 and 8 are supplementary     None                      2           5
                                                             1   3      4    6              s
  9. m5 = m10      k // m
                                                                       14
  10. m1 = m13    None
  Geometry/Trig                                    Name: __________________________
  Unit 3 Review Packet – Page 3 – Answer Key       Date: ___________________________
  Section V - Proofs                                                             J
  1.  Given: GK bisects JGI; m3 = m2                                    G    1       K
  Prove: GK // HI                                                               2
            Statements              Reasons
  1. GK bisects JGI            1. Given
  2. m1 = m2                  2. Definition of an Angles Bisector   H 3            I
  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       Prove: BD // FE                  A          C
     Statements                     Reasons
  1. AJ // CK              1. Given                            B         1       2   3     D
                                                                                4
  2. m1 = m3             2. If lines are parallel, then 
                           corresponding angles are 
                           congruent.                                            5
                                                             F                             E
  3. m1 = m5             3. Given                                J           K
  4. m3 = m5             4. Substitution
  5. BD // FE              5. If corresponding angles are 
                           congruent, then the lines are 
                           parallel.
  Geometry/Trig                                    Name: __________________________
  Unit 3 Review Packet – Page 4 – Answer Key       Date: ___________________________
  3.  Given: a // b; 3 @ 4              Prove:  10 @ 1   1                   2
                                                         a           3      4
      Statements                  Reasons                                5
  1. a // b                1. Given                                      6
                                                       b              7       8
  2. 4 @ 7               2. If lines are parallel then       10                     9
                           alternate interior angles
                           are congruent.                      c                        d
  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.                  b                   1    3
  Prove: m8 = m4                                                          4    5
                                                           a            6    7
          Statements                  Reasons                       8    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.