The SSS Rule

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 12 of 63.

The rule from the last lesson has a name: SSS, side side side. If three sides of one triangle are equal to three sides of another, the triangles are congruent. In a proof, the SSS line cites the three lines that give the three pairs of sides.

$Triangles ABC and DEF with three pairs of sides ticked equal$

Statement	Reason
1. AB = DE	Given
2. BC = EF	Given
3. CA = FD	Given
4. △ABC ≅ △DEF	SSS, using lines 1, 2 and 3

Write the congruence so the letters match the equal sides. The ticks pair AB with DE, so A and B must match D and E in order. Writing △ABC ≅ △EDF would put A on E and claim BC = DF and CA = FE, which the marks do not say.

Challenge

The tick marks pair the sides of △JKL and △PQR. The four statements of the proof are written; give each its reason and pick the lines it uses. Then press Check.

Try it yourself

$Write the proof$