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Similar triangle proofs worksheets

Similar triangles have the same shape at a different size, and a proof shows why. 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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Similar triangle proofs
Similar triangle proofs worksheet — AA, SAS~, SSS~ proofs, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The workhorse is AA. A line drawn parallel to one side of a triangle cuts off a smaller triangle with the same angles, and two equal angles are enough to make triangles similar — so most of these proofs start from a parallel line and reach AA. The reasons that get there are Corresponding Angles and Alternate Interior Angles, the two facts a parallel line hands you, plus the Reflexive Property for the angle a nested triangle shares with the whole.

Why this sheet works

SAS~ and SSS~ are the other two rules, and they are where similarity parts from congruence: the sides are in PROPORTION, not equal, so the given is a ratio like AD/AB = AE/AC rather than a pair of equal lengths. There are no equal-length tick marks on these figures for exactly that reason — an equal mark would say the wrong thing.

How this one works

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

Which reason completes the proof?

Step 2:∠ACD ≅ ∠B
∠ACD ≅ ∠B→Given
Given
  1. The proof is missing the reason for step 2: "∠ACD ≅ ∠B". Read what that step claims.
  2. This fact is handed to you in the Given — nothing has to justify it.
  3. So the missing reason is Given.

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