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Use Similar Right Triangles

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Juan Jorrin

on 23 May 2018

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Transcript of Use Similar Right Triangles

Use Similar Right Triangles
Excel Mathematics TV
Similar Right Triangles Theorem
"If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other."
GOAL!
Thank you!
Example
Identify the similar triangles in the diagram. ===>
Proportions Involving Geometric Means in Right Triangle ABC
Example
Geometric Means
Similar Right Triangles Theorem
Solution:
Sketch the three similar right triangles so that the corresponding angles and sides have the same orientation.
Example
Geometric Mean (Altitude) Theorem
In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments.

The length of the altitude is the geometric mean of the lengths of the two segments.
Geometric Mean (Leg) Theorem
In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments.

The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
Full transcript