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Vertical Angles in Proofs

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 37 of 63.

Two triangles that meet at a point where two segments cross form a bowtie. The two angles at the crossing, one in each triangle, are vertical angles, so they are equal. That gives you an angle pair for free, just as a shared side gives you a side pair.

$Segments AD and BE cross at C, making triangles ABC and DEC$

Here AD and BE cross at C. ∠ACB and ∠DCE sit opposite each other at the crossing, so ∠ACB = ∠DCE by Vertical angles. The line cites nothing: the crossing on the figure is the whole reason.

Challenge

Segments PR and QS cross at O. The two angles at O inside the triangles are highlighted. Pick the reason they are equal, then press Check.

Try it yourself

$Name the rule that links them$

Name the rule that links them

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Congruence & Proof

2Congruent Triangles

Same Size, Same Shape Matching Sides Matching Angles 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 ProofsThe 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