8.3. Inscribed Similar Triangles http://www.ck12.org
8.3 Inscribed Similar Triangles
Here you’ll learn how inscribed right triangles are similar and how to apply this in order to solve for missing
information.
What if you were told that, in California, the average home price increased 21.3% in 2004 and another 16.0% in
2005? What is the average rate of increase for these two years? After completing this Concept, you will be able to
use the geometric mean to help solve this problem.
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52505CK-12 Foundation: Chapter8InscribedSimilarTrianglesA
Learn more about similar triangles in right triangles by watching the second part of this video.
Guidance
If two objects are similar, corresponding angles are congruent and their sides are proportional in length. Let’s
look at a right triangle, with an altitude drawn from the right angle. There are three right triangles in this picture,
4 ADB, 4 CDA, and 4 CAB. Both of the two smaller triangles are similar to the larger triangle because they each
share an angle with 4 ADB. That means all three triangles are similar to each other.
Inscribed Triangle Theorem:If an altitude is drawn from the right angle of any right triangle, then the two triangles
formed are similar to the original triangle and all three triangles are similar to each other.
You are probably familiar with the arithmetic mean, whichdivides the sumofnnumbers byn. This is commonly
used to determine the average test score for a group of students. The geometric mean is a different sort of average,
which takes thenthroot of the productofnnumbers. In this text, we will primarily compare two numbers, so we
would be taking the square root of the product of two numbers. This mean is commonly used with rates of increase
or decrease.
Geometric Mean:The geometric mean of two positive numbersaandbis the numberx, such thatax=xborx^2 =ab
andx=
√
ab.