More Geometry Proofs

University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2021
Views:

275

Pages:

10
Author:

tristepeon32s

Warm-Up If it is July, then it is summer Hypothesis: It is July Conclusion: It is summer Converse: It it is summer, then it is July Is there counterexample that would prove the converse false? It is August Example 5: Given: RS = PS and ST = SQ R. S P Prove: RT = PQ Q T Statements Reasons 1. RS = PS 1. Given 2. 2. Addition Property 3. ST = SQ 3. 4. 4. Substitution 5. 5. Segment Addition Postulate 6. RT = PQ 6. Given: m angle4+m angle 6 = 180 Prove: m angle5=m angle6 4 5 6 Statements Reasons 1. m angle4+m angle 6 = 180 1. Given 2. m angle4+m angle 5 = 180 2. Angle Add. Post. /Def. of Linear Pair 3. m angle4+m angle5=m angle4+m angle6 3. Substitution 4. m angle4=m angle4 4. Reflexive 5. m angle5=m angle6 5. Subtraction Given: m angle1=m angle3 m angle2=m angle4 C 2 B F 4 3 Prove: m angle ABC =m angle DEF A 1 E D Statements Reasons 1. m angle1=m angle3; m angle2=m angle4 1. Given 2. m angle1+m angle2=m angle3+m angle4 2. Addition Prop. 3. m angle1+m angle2=m angle ABC m angle3+m angle4=m angle DEF 3. Angle Addition Postulate 4. m angle ABC =m angle DEF 4. Substitution