Corresponding Angles in Proofs
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 44 of 63.
When a triangle slides along a line, its sides stay parallel to where they were. Each side and its moved copy are parallel lines cut by the line the triangle slides along, so their angles with that line are corresponding angles.
| Statement | Reason |
|---|---|
| 1. AE ∥ CF | Given |
| 2. BE ∥ DF | Given |
| 3. AB = CD | Given |
| 4. ∠EAB = ∠FCD | Corresponding angles, using line 1 |
| 5. ∠EBA = ∠FDC | Corresponding angles, using line 2 |
| 6. △ABE ≅ △CDF | ASA, using lines 3, 4 and 5 |
Two different pairs of parallel lines are in play, so each corresponding angles line cites its own pair. Citing the wrong one is a common slip, and the board points it out.
Challenge
K, L, M and N lie on one line. The chevrons show KO ∥ MP and LO ∥ NP, and the ticks show KO = MP. Prove that △KLO ≅ △MNP, 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