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Geometric Mean and Similarity in Right Triangles, Slides of Geometry

The concept of the geometric mean between two numbers and its application in right triangles. It also derives the relationship between the sides of a right triangle when an altitude is drawn to the hypotenuse, leading to the similarity of the formed triangles. Examples and a theorem.

What you will learn

  • What is the geometric mean between two numbers?
  • How is the geometric mean related to the sides of a right triangle when an altitude is drawn to the hypotenuse?

Typology: Slides

2021/2022

Uploaded on 09/27/2022

oliver97
oliver97 🇺🇸

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Similarity in Right
Triangles
Goals:
·Determine the geometric mean between two
numbers
·State and apply the relationship that exist when
the altitude is drawn to the hypotenuse of a
right triangle.
What are the terms x and y in the proportion shown called?
If a, b, and x are positive numbers and then x is called the
geometric mean between a and b.
Geometric mean - the result when you multiply two numbers and take
the square root.
What is the geometric mean?
pf3
pf4

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Similarity in Right

Triangles

Goals:

· Determine the geometric mean between two

numbers

· State and apply the relationship that exist when

the altitude is drawn to the hypotenuse of a

right triangle.

What are the terms x and y in the proportion shown called? If a , b , and x are positive numbers and then x is called the geometric mean between a and b. Geometric mean - the result when you multiply two numbers and take the square root. What is the geometric mean?

Examples: Find the geometric mean between the following:

  1. 4 and 25 2) 2 and 3 3) 8 and 27 When the altitude is drawn to the hypotenuse of a right triangle, · The length of the altitude is the geometric mean between the segments of the hypotenuse · Each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg. a b c d e

Identify the three triangles: Small - Medium - Large - 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. List all proportions for each pair of similar triangles.