Identify Similar Triangles with Proofs Worksheets
How to Identify Similar Triangles with Proofs - Similar figures are those that have the same shape but different sizes. We can easily identify similar triangles by applying three similarity theorems specific to triangles. These three theorems involve, side-angle -side (SAS), Angle- Angle (AA), and Side-Side-Side (SSS). The three similarity theorems of a triangle depend upon the corresponding parts. That means that you take the measurements of one triangle and compare the same with the other triangle. You can also develop ratios of lengths, and if ratios are congruent, then corresponding sides are similar. Moreover, you need to consider the included angle while comparing the lengths or ratio of lengths of two triangles. Angle-Angle (AA) Theorem - Angle-Angle (AA) theorem says that two triangles are similar if the two pairs of their corresponding angles are congruent. These two triangles might appear as identical. To establish two triangles as congruent using this theorem, you only have to compare the two pairs of corresponding angles. Side-Angle-Side (SAS) Theorem - This theorem follows the order of a side, an included angle, and then a side. The SAS theorem says that two triangles are similar if two sides of a triangle are proportional to the two corresponding sides of second triangles, and the included angles are congruent. Side-Side-Side (SSS) Theorem - The last theorem telling us about the congruency of a triangle, states that if all three sides of one triangle are proportional to all three corresponding sides of the second triangle, then those two triangles are congruent.
The Pythagorean Theorem states,
"In a right triangle, the square of the hypotenuse equals the sum of the squares of the 2 other sides." Other civilizations knew it long before Pythagoras, but he generalized it and made it popular.