1 / 5

Practice for Proofs of: Parallel Lines Proving Converse of AIA, AEA, SSI, SSE

Practice for Proofs of: Parallel Lines Proving Converse of AIA, AEA, SSI, SSE. By Mr. Erlin Tamalpais High School 10/20/09. r. Converse of Alternate Interior Angles Theorem. Given :. Statement Reason. 1. 2. p. 3. 4. 5. 6. Prove : p is parallel to q. q. 7. 8.

regan-buchanan
Download Presentation

Practice for Proofs of: Parallel Lines Proving Converse of AIA, AEA, SSI, SSE

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Practice for Proofs of: Parallel LinesProving Converse of AIA, AEA, SSI, SSE By Mr. Erlin Tamalpais High School 10/20/09

  2. r Converse of Alternate Interior Angles Theorem Given: Statement Reason 1 2 p 3 4 5 6 Prove: p is parallel to q q 7 8 & 4  5 • 4  5 • 4 & 5 are alt interior angles • 1 & 4 are vertical angles • 1  4 • 1  5 • 1 & 5 are Corresponding Angles • r is a transversal over p, q • p is parallel to q • Given • Given/Definition of AlA • Definition of Vertical Angles • If Vertical Angles, then  • Transitive Prop  • Definition of Corresponding Angles. • Given/Definition of Transversal • If lines cut by a transversal form corresponding angles that are , then lines are parallel QED

  3. r Converse of Alternate Exterior Angles Theorem Given: Statement Reason 1 2 p 3 4 5 6 Prove: p is parallel to q q 7 8 & 1  8 • Given • Given/Definition of AEA • Definition of Vertical Angles • If Vertical Angles, then  • Symmetric Prop  • Transitive Prop of  • Definition of Corresponding Angles. • Given/Definition of Transversal • If lines cut by a transversal form corresponding angles that are , then lines are parallel • 1  8 • 1 & 8 are alt exterior angles • 1 & 4 are vertical angles • 1  4 • 4  1 • 4  8 • 4 & 8 are Corresponding Angles • r is a transversal over p, q • p is parallel to q QED

  4. Converse of Same Side Interior Angles are Supplementary transversal corresponding congruent lines are parallel. r Given: Statement Reason 1 2 p Prove: Line p is parallel to line q 3 4 5 6 q and: 3 &5 are supplementary • Given • Given • Definition of Supplementary • Definition of Linear Pair • If Linear Pair, then Supplementary • Definition of Supplementary • Substitution Prop. of Equality • Subtraction Prop. of Equality • Definition of Congruent Angles • Definition of Corresponding s • If then • r is a transversal to p, q • 3 & 5 are Supplementary • m3 + m5= 180 • 3 and 1 form a Linear Pair • 3 & 1 are Supplementary • m3 + m1 = 180 • m3 +m5= m3 + m1 • m5=m1 • 51 • 5 & 1 are Corresponding s • p is parallel to q QED

  5. Converse of Same Side Exterior Angles are Supplementary transversal corresponding congruent lines are parallel. r Given: Statement Reason 1 2 p Prove: Line p is parallel to line q 3 4 5 6 q 7 and: 1 &7 are supplementary • Given • Given • Definition of Supplementary • Definition of Linear Pair • If Linear Pair, then Supplementary • Definition of Supplementary • Substitution Prop. of Equality • Subtraction Prop. of Equality • Definition of Congruent Angles • Definition of Corresponding s • If then • R is a transversal to P, Q • 1 & 7 are Supplementary • m1 + m7= 180 • 3 and 1 form a Linear Pair • 3 & 1 are Supplementary • m3 + m1 = 180 • m1 +m7 = m3 + m1 • m7=m3 • 73 • 7 & 3 are Corresponding s • P is parallel to Q QED

More Related