Puzzle Given:  1 and  5 are supplementary.  3 and  5 are supplementary. Prove: m  1 = m  3 Statements Reasons Q P R ST U Given : m  SQT =  m  TQU Prove: m  SQT = m  RQP StatementsReasons Puzzle 2

3 12 Given:  1 and  2 are vertical angles. Prove: m  1 = m  2 (NOTE: This is the proof for the Theorem – Vertical Angles are Congruent – Therefore, you CANNOT use this theorem as a reason within this proof.) StatementsReasons Proof Puzzle 3 Statements Reasons Given:  1 and  2 are supplementary.  3 and  4 are supplementary.  m  2  =  m  4 Prove: m  1 = m  3 Puzzle 4

Puzzle Proof 5 Given: m  1 = m  3 m  ABC = m  JKL Prove: m  2 = m  C B K A J L Puzzle Proof 6 Given: AB = BE BC = DB Prove: AC = DE D A B E C Statements Reasons StatementsReasons D M

Statements & Reasons for Puzzles 1, 2, and 3 m  5 = m  5  1 and  5 are supplementary.  3 and  5 are supplementary. m  1 + m  5 = m  3 + m  5 m  1 = m  3 m  1 + m  5 = 180  m  3 + m  5 = 180  m  1 = m  5  1 and  2 are vertical angles. m  1 = m  2 m  1 + m  3 = 180  m  2 + m  3 = 180  m  1 + m  3 = m  2 + m  3 m  1 + m  2 = m  3 m  3 = m  3 Substitution Vertical Angles are Congruent Given Reflexive Subtraction Definition of Supplementary Angles m  SQT = m  TQU m  RQP + m  PQU = 180 m  TQU = m  RQP m  SQT + m  TQU = m  SQU m  SQT = m  RQP Puzzle 1 Puzzle 2 Angle Addition Postulate Given Vertical Angles are Congruent Definition of Vertical Angles Substitution Definition of Supplementary Angles Puzzle 3 Angle Addition Postulate Given Subtraction Definition of Vertical Angles Substitution Reflexive Definition of Supplementary Angles

Given Angle Addition Postulate Addition Property Subtraction Property Definition of Supplementary Angles Substitution Given Angle Addition Postulate Segment Addition Postulate Addition Property Subtraction Property Vertical Angles are Congruent Substitution m  1 = m  3 m  1 + m  2 = m  3 + m  4  1 and  2 are supplementary.  3 and  4 are supplementary. m  1 + m  2 = 180° m  3 + m  4 = 180° m  2 = m  4 m  1 = m  4 Statements & Reasons for Puzzles 4, 5, and 6 Puzzle 4 Puzzle 5 Puzzle 6 Given Definition of Complementary Angles Definition of Supplementary Angles Angle Addition Postulate Substitution Subtraction m  1 = m  3 m  2 = m  4 m  1 + m  2 = m  ABC m  3 + m  4 = m  JKL m  ABC = m  JKL m  1 + m  2 = 180 m  3 + m  4 = 180 m  1 + m  2 = m  3 + m  4 AB = BEBC = DB AC = DE AB + BC = AC BE + DB = DE AB + BC = BE + DB m  ABE = m  DBC