Linear Pairs in Proofs
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 40 of 63.
Two angles side by side on a straight line add up to 180°. In a proof this is written as a supplementary pair, with the reason Linear pair. Like vertical angles, it needs no earlier line: the straight line on the figure is the reason.
Linear pairs pay off with a third rule, Supplements of equal angles: if two angles are equal, the angles that make 180° with them are equal too. Each is 180° minus the same amount. The two equal angles may even be one and the same angle.
| Statement | Reason |
|---|---|
| 1. ∠AEB and ∠BEC are supplementary | Linear pair |
| 2. ∠BEC and ∠CED are supplementary | Linear pair |
| 3. ∠AEB = ∠CED | Supplements of equal angles, using lines 1 and 2 |
Both ∠AEB and ∠CED make 180° with the same angle, ∠BEC, so they are equal. That is exactly why vertical angles are equal. When the two angles you start from are given equal rather than the same, the line cites that given too.
Challenge
Rays KM and OP stand on the straight lines JL and NQ. The angles MKJ and PON are marked equal. Prove that ∠MKL = ∠POQ, 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 Angles