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Corresponding Angles in Proofs

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 41 of 60.

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.

$Points A, B, C, D on a line; triangles ABE and CDF with AE parallel to CF and BE parallel to DF$

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

$Write the proof$

Write the proof

All lessons in Congruence & Proof

2Congruent Triangles

Same Size, Same Shape What Congruence Gives Recap: Matching Parts

5ASA and AAS

The Side Between The ASA Rule The AAS Rule ASA or AAS?Recap: ASA and AAS

8Proofs with Vertical Angles

Vertical Angles in Proofs The Bowtie Bowtie with ASA Linear Pairs in Proofs Recap: Vertical Angles

11Similarity Proofs

AA Similarity Two Right Triangles SSS Similarity SAS Similarity Similar, Then Find Recap: Similarity

3SSS

Three Sides Fix It The SSS Rule A Shared Side SSS with a Shared Side Recap: SSS

6HL for Right Triangles

Hypotenuse and Legs The HL Rule Why HL Works HL with a Shared Leg Recap: HL

9Proofs with Parallel Lines

Parallel Angles as Reasons Alternate Angles in a ProofCorresponding Angles in ProofsParallel or Not?Recap: Parallel Proofs

12Final Challenges

Final: The Kite Diagonals Final: Overlapping Triangles Final: Enough to Find It?Final: The Height Bisects Final: The Roof Frame