Question

Daniel claims that any two right triangles can be proven to be similar by the sas similarity theorem because both have right angles that are congruent. what is his mistake?

Answer 1

SAS similarity theorem: When two triangles have corresponding angles that are congruent and corresponding sides with identical ratios, the triangles are similar.
Two right angles are always congruent, but corresponding sides not always have identical ratios. For example, first right triangle has two legs of 3 and 4 lengths. Second triangle has two legs of 5 and 12 lengths. Then $\frac{3}{5} \neq \frac{4}{12}$. That is the mistake.

Answer 2

Daniel has not satisfied all the conditions of the theorem. The corresponding sides of each of the right triangles must also be in proportion for the triangles to be similar.