Your First Full Proof

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 4 of 63.

Now you write every line yourself. A good way to plan is backwards: look at what you must prove, and ask which rule could give it. Then ask what that rule needs, and keep going until you reach the given.

$An angle a arc-marked equal to angle b; angle c is vertical to angle b$

Here the arcs say ∠a = ∠b, and the task is to prove ∠c = ∠a. Working backwards: the transitive property would give it, if ∠c and ∠a were both linked to ∠b. The arcs link ∠a. Vertical angles link ∠c, because ∠b and ∠c sit opposite each other where two lines cross.

Statement	Reason
1. ∠a = ∠b	Given (the arcs)
2. ∠b = ∠c	Vertical angles
3. ∠c = ∠a	Transitive property, using lines 1 and 2

Vertical angles need no earlier line: the crossing on the figure is the reason. On the board, tap the two angles to write the statement, pick the reason, and cite lines when the reason uses them.

Challenge

Two pairs of lines cross. The arcs say ∠1 = ∠2. Prove that ∠3 = ∠4. Write each line by tapping the two angles, pick its reason, cite the lines it uses, then press Check.

Try it yourself

$Write the proof$