The similar-triangle proof sheets hide one reason and let a child choose it; this is the next step, where the table is empty and the whole argument is theirs to write. A diagram, a Given, a Prove — and room to build a similarity proof from nothing.
Where the congruence version of this sheet finishes on SSS, SAS, ASA or AAS, this one ends on the similarity rules: AA, SAS~ or SSS~. Most arguments start from a line drawn parallel to one side of a triangle, which hands a child Corresponding or Alternate Interior Angles, and two equal angles are enough — that is AA. The Reflexive Property supplies the angle a nested triangle shares with the whole.
Why this sheet works
This is a written worksheet, not an online exercise, for the reason every proof sheet is: a proof has many valid orderings and wordings, so it cannot mark itself. The answer key is the model — every statement and the reason it rests on, written out in full — which is exactly what a child checks their own argument against.
How this one works
One question from this sheet, worked through a step at a time.
Prove △RUV ~ △RST
Prove:△RUV ~ △RST
1. ∠R ≅ ∠R→Reflexive Property
2. RU/RS = RV/RT→Given
3. △RUV ~ △RST→SAS ~
You are given RU/RS = RV/RT, and you have to prove △RUV ~ △RST. Build it one line at a time — each line is a statement and the reason it is true.
1. ∠R ≅ ∠R — A segment (or angle) is congruent to itself. The two triangles share this side, so it is equal in both by the reflexive property.
2. RU/RS = RV/RT — This fact is handed to you in the Given — nothing has to justify it.
3. △RUV ~ △RST — One pair of angles is equal and the two sides around it are in proportion: SAS similarity.
That is the whole proof: the last line, △RUV ~ △RST, follows by SAS ~.
