The Bowtie

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 35 of 60.

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.

$Bowtie: AC and CD ticked once, BC and CE ticked twice$

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

$Write the proof$

Write the proof

All lessons in Congruence & Proof

2Congruent Triangles

5ASA and AAS

8Proofs with Vertical Angles

11Similarity Proofs