Parallel Angles as Reasons
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 42 of 63.
The parallel line rules from the Angles section are proof reasons too: Corresponding angles, Alternate interior angles and Alternate exterior angles give equal angles, and Co-interior angles give a supplementary pair. Each one only holds when the lines are parallel, so its line cites the line that says so.
| Statement | Reason |
|---|---|
| 1. AB ∥ CD | Given (the chevrons) |
| 2. ∠MAB = ∠MDC | Alternate interior angles, using line 1 |
The angles at A and D sit inside the parallel lines, on opposite sides of the crossing segment AD: an alternate pair. Without line 1 the step would not follow, because without parallel lines alternate angles need not be equal. The proof menu calls this rule Alternate interior angles; the angle menus you know from the Angles section call it Alternate angles.
Challenge
PQ is parallel to RS, and segments PS and QR cross at O. The angles at Q and R are highlighted. Pick the reason they are equal, then press Check.
Try it yourself
Name the rule that links them
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