How Do You Find Unknown Lengths (Sides) Of A Similar Triangle Using Euclids Theorem?
Learn how to find unknown lengths (sides) of a similar triangle using Euclid’s theorem. WHAT IS A TRIANGLE? A triangle is a polygon with positive interior angles which always add up to 180°. WHAT IS A SIMILAR TRIANGLE? Two triangles are similar if they have two angles that are the same… If this is the case the third angle will also be the same since the interior angles of triangles always add up to 180°. If two triangles are similar, they’re corresponding sides are proportional. EUCLID’S THEOREM: a/a^’ = b/b^’ = c/c^’ [EXAMPLE PROBLEM] Find the height of a tree. The tree cast a shadow 65ft long, while at the same time a much shorter tree with a height of 11ft cast a shadow 5ft long. [REMEMBER] Since the measurements were taken at the same time, the sun cast shadows with the same angle on both trees. Also, both trees are growing straight up at 90° angles… Because both trees share the same two angles they form similar triangles and therefore have sides proportional to each other. [SO
