 Similar right triangles formed by dropping an altitude--explained using an interactive applet, a you tube video step by step example problems. Similar Right Triangles. Definitions: Right Triangle - A triangle that has a right angle in its interior. Geometric Mean - The geometric mean of two positive numbers. A right triangle (American English) or right-angled triangle (British English) is a triangle in which the hypotenuse then the triangle is divided into two smaller triangles which are both similar to the original and therefore similar to each other. Author: Mrs. Alec Walker Country: Russia Language: English Genre: Education Published: 14 August 2014 Pages: 301 PDF File Size: 48.13 Mb ePub File Size: 50.5 Mb ISBN: 501-6-59446-302-7 Downloads: 57165 Price: Free Uploader: Mrs. Alec Walker Before we state these theorems, let's take a look at a theorem relating to the triangles we will be using: The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle.

Let's separate the diagram, and move the sections around so we can more clearly see the similar triangles involved. Since these triangles are similar, we can establish a series of proportions right triangle similarity their corresponding sides.

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Prove that two similar right triangles are similar. Diagram 2 Exploration Moving on to Diagram 2 on the handout, I ask the students to outline the three triangles in different colors.

Similar Right Triangles side lengths

Then I ask them to label the sides. We repeat this process with the middle-sized triangle and then the big triangle which always leads me to make dumb references to Goldilocks and the Three Bears.

At this point, we take a step back and look at the diagram as a whole. What do they notice aboutfor example? Click on the reflected triangle and choose rotate in the transform menu. Similarity of triangles is transitive.

Similar Right Triangles

The altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse creates two triangles, both of which are similar to the original right triangle similarity and each other. Since these triangles are similar, we can establish a series of proportions relating their corresponding sides. Two valuable theorems are formed using 3 of these proportions: Remember the "look" of the given diagram for this theorem. If you right triangle similarity the rules stated in the following theorems, you can simply recall this original diagram and set up the corresponding sides of the three similar triangles.

Mark C as center in the transform menu. Click on the reflected triangle and choose rotate in the transform menu. Similarity of triangles is transitive.