Chaining Equal Parts

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 2 of 60.

∠1 = ∠2, and ∠2 = ∠3. So ∠1 = ∠3. You do not need to look at ∠1 and ∠3. Both are equal to ∠2, so they are equal to each other.

This is the Transitive property: if a = b and b = c, then a = c. It works for sides and for angles.

Proofs use it often. One rule links the first part to a middle part. Another rule links the middle part to the last part. Then the transitive property links the first part to the last. Its line names the two lines it uses.

Challenge

The arcs say ∠1 = ∠2. ∠2 and ∠3 are vertical angles: they face each other where two lines cross. The first two lines are already written. Add the line that proves ∠1 = ∠3. Then press Check.

Try it yourself

$Write the proof$