Your First Full Proof

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 3 of 60.

Two pairs of lines cross in two places, far apart. The lines lean in different directions. The arcs say ∠1 = ∠2. Can you be sure that ∠3 = ∠4 without measuring?

Plan the proof from the end. Which rule can give ∠3 = ∠4? The transitive property can, if ∠3 and ∠4 are linked to two equal angles. ∠3 and ∠1 face each other at one crossing. Angles like these are vertical angles, and they are equal. ∠4 and ∠2 are vertical angles too. Then write the proof from the start, with the given fact first.

Challenge

Two pairs of lines cross. The arcs say ∠1 = ∠2. Prove that ∠3 = ∠4. For each line, tap its two angles, pick its reason and choose the lines it uses. Then press Check.

Try it yourself

$Write the proof$