Congruent, Then Equal

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 32 of 63.

Most proofs about a side or an angle follow one plan. Find two triangles that contain the parts you care about, prove those triangles congruent, then finish with CPCTC. The congruence is the middle of the proof, not the end.

$Quadrilateral PQRS with opposite sides ticked equal and the diagonal PR$

Statement	Reason
1. PQ = RS	Given
2. QR = SP	Given
3. PR = PR	Reflexive property
4. △PQR ≅ △RSP	SSS, using lines 1, 2 and 3
5. ∠PQR = ∠RSP	CPCTC, using line 4

Nothing marks the angles at Q and S, yet they are proved equal. They are matching parts of the two triangles the diagonal makes, so the congruence hands them over.

Challenge

△JKL and △JKM share the side JK. The ticks show KL = KM, and the angles at K are marked equal. The first four statements are written. Give each its reason, add the line that proves JL = JM, then press Check.

Try it yourself

$Write the proof$