3 ­ Notes ­ Altitude on Hypotenuse Theorems.notebook
September 19, 2016
Altitude on Hypotenuse
Theorems
MGSE9‐12.G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor.
a. The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.
MGSE9‐12.G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
MGSE9‐12.G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Aug 15­6:17 PM
What am I learning today?
The definition of similar figures and how to use their properties to solve figures.
How will I show that I learned it?
Verify that two figures are similar and find the scale factor of the dilation.
Aug 15­6:19 PM
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3 ­ Notes ­ Altitude on Hypotenuse Theorems.notebook
September 19, 2016
To find the Geometric Mean of n numbers:
1) Find their product
2) Take the nth root of this product
Find the geometric mean of 4 and 16
Sep 17­1:25 PM
In the proportion
a and d are called the extremes b and c are called the means If the means of a proportion are equal, then they represent the geometric mean of the extremes
Sep 17­1:33 PM
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3 ­ Notes ­ Altitude on Hypotenuse Theorems.notebook
September 19, 2016
What happens when an altitude is drawn to the hypotenuse in a right triangle?
A
C
B
Sep 17­1:45 PM
Because of these similarities, we can conclude two "Altitude on Hypotenuse" Theorems:
Altitude on Hypotenuse Theorem 1
In any right triangle, the altitude from the right angle is the geometric mean between the two segments of the hypotenuse
A
D
B
C
Sep 17­1:43 PM
3
3 ­ Notes ­ Altitude on Hypotenuse Theorems.notebook
September 19, 2016
Altitude on Hypotenuse Theorem 2
In any right triangle, the length of each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse adjacent to that leg.
A
D
C
B
Sep 17­2:41 PM
x
10
6
Sep 17­2:51 PM
4
3 ­ Notes ­ Altitude on Hypotenuse Theorems.notebook
September 19, 2016
5
x
18
Sep 17­2:51 PM
10
x
21
Sep 17­2:58 PM
5
3 ­ Notes ­ Altitude on Hypotenuse Theorems.notebook
September 19, 2016
Proof of Pythagorean Theorem using Similarity
A
Given: is a right triangle with right angle B
Prove: C
B
Oct 2­10:42 AM
What is Ms. Morton looking for when grading tests/quizzes/skills checks?
1. Clear work
2. Equations that demonstrate your knowledge of geometric properties
3. Answer clearly stated
4. Correct notation and units
5. Answers for all intermediate variables
Sep 19­9:28 AM
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