Alternate Angles in a Proof
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 43 of 63.
Parallel lines and a bowtie together make a Z-shaped figure that appears in many proofs. The parallel lines give alternate angle pairs, and the crossing gives vertical angles.
| Statement | Reason |
|---|---|
| 1. AB ∥ CD | Given |
| 2. AB = CD | Given |
| 3. ∠MAB = ∠MDC | Alternate interior angles, using line 1 |
| 4. ∠MBA = ∠MCD | Alternate interior angles, using line 1 |
| 5. △ABM ≅ △DCM | ASA, using lines 2, 3 and 4 |
The side AB joins the two angles at A and B, so ASA fits. The matching is A to D and B to C, because the alternate pairs pair those corners.
Challenge
EF is parallel to HJ, and segments EJ and FH cross at G. The ticks show EG = JG. Prove that △EFG ≅ △JHG, then press Check.
Try it yourself
Write the proof
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Congruence & Proof
1What a Proof Is
Given and ProveStatements and ReasonsChaining Equal PartsYour First Full ProofRecap: A Chain of Reasons2Congruent Triangles
Same Size, Same ShapeMatching SidesMatching AnglesWhat Congruence GivesRecap: Matching Parts8Proofs with Vertical Angles
Vertical Angles in ProofsThe BowtieBowtie with ASALinear Pairs in ProofsRecap: Vertical Angles9Proofs with Parallel Lines
Parallel Angles as ReasonsAlternate Angles in a ProofCorresponding Angles in ProofsParallel or Not?Recap: Parallel Proofs