The Bowtie
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 38 of 63.
A bowtie with two pairs of ticks is an SAS figure. The ticks give the two side pairs, and the vertical angles at the crossing sit between them.
| Statement | Reason |
|---|---|
| 1. AC = DC | Given |
| 2. BC = EC | Given |
| 3. ∠ACB = ∠DCE | Vertical angles |
| 4. △ABC ≅ △DEC | SAS, using lines 1, 2 and 3 |
Check the included angle: in △ABC the sides AC and BC meet at C, and the vertical angle is at C. The matching sends C to C, A to D and B to E.
Challenge
Segments KN and LO cross at M. The ticks show KM = NM and LM = OM. Prove that KL = NO, 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