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Triangle congruence proofs worksheets

A proof is a chain of statements, each resting on a reason. These free printable worksheets give a diagram, a Given and a Prove, and a two-column proof with one reason hidden — the child reads the argument and names the missing justification.

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Triangle congruence proofs
Triangle congruence proofs worksheet — Two-column proofs, reason bank, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The reasons are a small, fixed vocabulary, and knowing them is the skill the standard is after: Given for a stated fact, the Reflexive Property for a side a triangle shares with its neighbour, Vertical Angles for a crossing, Alternate Interior Angles for parallel lines, the Definition of a Midpoint for a bisected segment, and one of SSS, SAS, ASA or AAS for the line that finishes the proof.

Why this sheet works

The step that trips a child is the last one. Which criterion the statements add up to depends on WHICH parts were shown equal and whether the equal angle sat between the two equal sides — SAS — or the equal side sat between the two equal angles — ASA. Reading the three statements above the blank in order is what answers it, and the proof is laid out so that reading is possible.

How this one works

One question from this sheet, worked through a step at a time.

Which reason completes the proof?

Step 1:∠ADB and ∠ADC are right angles
∠ADB and ∠ADC are right angles→Definition of Perpendicular
Definition of Perpendicular
  1. The proof is missing the reason for step 1: "∠ADB and ∠ADC are right angles". Read what that step claims.
  2. Perpendicular lines meet at a right angle — that is what 'perpendicular' means — so the angles where they cross are right angles.
  3. So the missing reason is Definition of Perpendicular.

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