Check Similarity in Right Triangles Calculator

Two triangles are considered similar if their corresponding angles are equal and their corresponding side lengths are proportional. For right triangles, because one angle is always 90 degrees, you only need to prove that one acute angle matches, or that the ratio of the legs is equal (SAS theorem), or that all three corresponding side ratios are equal (SSS theorem). The foundational relationship governing right triangle sides is the Pythagorean theorem: c^2 = a^2 + b^2. When comparing Triangle 1 to Triangle 2, a consistent scale factor (k) must exist such that a_2 = k * a_1, b_2 = k * b_1, and c_2 = k * c_1.

Imagine Triangle 1 has a leg a = 3 and a leg b = 4. Using the Pythagorean theorem, its hypotenuse is c = sqrt(3^2 + 4^2) = 5. Now, suppose Triangle 2 has a leg a = 6 and a leg b = 8. To check for similarity, we calculate the scale factor for each leg: 6 / 3 = 2, and 8 / 4 = 2. Because both legs scale by the exact same factor of 2, the triangles are similar. The hypotenuse of Triangle 2 will automatically scale to 5 * 2 = 10, confirming a valid 3-4-5 to 6-8-10 similarity ratio.

Always ensure you are comparing corresponding sides—never compare a base leg to a hypotenuse. When verifying side ratios, compute all fractions to their simplest decimal form to easily spot uniform scaling. Keep in mind that sharing a single acute angle is sufficient to prove right triangle similarity due to Angle-Angle (AA) similarity postulates.