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Geometry Lesson

Triangle Congruence Criteria: From Recognition to Proof

Shared by A STEM Educator

High SchoolThin-SlicingCCSS.MATH.CONTENT.HSG.CO.B.8, CCSS.MATH.CONTENT.HSG.CO.C.1050 min
Learning Objective

Students will identify sufficient conditions for triangle congruence (SSS, SAS, ASA, AAS, HL), justify their reasoning with congruence criteria, and write structured two-column proofs using given information and geometric properties.

Lesson Overview

Students progress from identifying congruent parts in labeled triangles, to naming the correct congruence criterion, to constructing two-column proofs — changing only one variable of complexity at a time across six tasks.

Materials

  • Vertical whiteboards or chart paper
  • Dry-erase markers (multiple colors)
  • Random grouping tool
  • Printed consolidation note sheets
  • Rulers and protractors (optional, for launch)

Scaffolded Task Progression

1Task 1
The two triangles below have their congruent parts marked. List every pair of congruent sides and angles you can see from the tick marks. Do you think the triangles are congruent? Why or why not? ```geometry {"figureType":"triangle","angles":{"A":55,"B":65},"vertexLabels":["A","B","C"],"showAngles":true,"title":"Triangle 1"} ``` ```geometry {"figureType":"triangle","angles":{"A":55,"B":65},"vertexLabels":["D","E","F"],"showAngles":true,"title":"Triangle 2"} ``` Both triangles have: $\angle A = \angle D = 55°$, $\angle B = \angle E = 65°$, $\angle C = \angle F = 60°$. Are three pairs of congruent angles enough to guarantee congruence?
2Task 2
Now three SIDE lengths are given. Decide: is there exactly one triangle possible, or could there be more than one?

Triangle 1: , , .
Triangle 2: , , .

If , , and , what congruence criterion applies? Write the congruence statement.

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