L2 · Congruence statements and corresponding parts

Learning goal

“I can read a congruence statement as a vertex-by-vertex matching: extract all three pairs of equal sides and all three pairs of equal angles from it, use it to find unknown measures, and write a correct statement for two triangles whose data is given in scrambled order.”

Congruence statement — the written claim triangle ABC is congruent to triangle RST; its power is that position encodes matching: 1st matches 1st, 2nd matches 2nd, 3rd matches 3rd.

Corresponding vertices — the matched corners: in triangle ABC congruent to triangle RST, A corresponds to R, B to S, C to T.

Corresponding sides — sides joining corresponding vertices: AB corresponds to RS, BC to ST, CA to TR - equal in length.

Corresponding angles — angles at corresponding vertices: angle A corresponds to angle R, and so on - equal in measure.

Worked example

You are told triangle ABC is congruent to triangle RST, and triangle ABC has AB = 5, BC = 9, CA = 7, angle A = 40 degrees, angle B = 100 degrees, angle C = 40 degrees. Step 1: Read the correspondence off the positions: A matches R, B matches S, C matches T. Step 2: Sides: AB joins the 1st and 2nd vertices, so AB = RS = 5. BC joins 2nd and 3rd: BC = ST = 9. CA joins 3rd and 1st: CA = TR = 7. Step 3: Angles sit AT vertices: angle A = angle R = 40 degrees, angle B = angle S = 100 degrees, angle C = angle T = 40 degrees. (Sanity check: 40 + 100 + 40 = 180 in both triangles.) Say it plainly: a congruence statement is a compressed file. Unzip it by position - vertex to vertex, then sides by their endpoints, then angles by their vertices - and all six equalities fall out without measuring anything.

Check yourself — explain it

In triangle ABC congruent to triangle RST, side CA equals TR (not RS) because...

Paired problem — example still visible

Given triangle MNO is congruent to triangle XYZ and MN = 6, which side of triangle XYZ measures 6? -> XY (M and N are 1st and 2nd; X and Y are 1st and 2nd)

Faded completion — last step is yours

"Triangle PQR is congruent to triangle STU: angle Q corresponds to angle ___" -> T (2nd vertex to 2nd vertex)

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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