Transcript Lesson_7.4_Similarity_in_Right_Triangles[1] - Mustang-Math

“What we do in life echoes in eternity.”
7.4 Similarity in Right Triangles
Similarity in Right Triangles
m1  m4  m7
m2  m6  m8
m3  m5  m9
Similarity in Right Triangles
Theorem 7-3: The altitude to the hypotenuse of a right triangle
divides the triangles into two triangles that are similar to the original
triangle and to each other.
Geometric Mean
Review: How do we find the arithmetic mean of 3 and 27?
a x
Geometric Mean: The number x such that  , where a, b, and x
x b
are positive numbers
Find the geometric mean of 3
and 27.
Find the geometric mean of 4

and 18.
Note: x  ab
Geometric Mean
6.75in
5.2 in
8.75in
Corollary to Theorem 7-3: The length of the altitude to the
hypotenuse of a right triangle is the geometric mean of the lengths
of the segments of the hypotenuse
Proof of Corollary to Theorem 7-3
C
Given : Right triangle, ABC, with
CD the altitude to the hypotenuse
Prove :
AD CD

CD DB
A
Statements
1. Right triangle, ABC, with
D
B
Reasons
1.
CD the altitude to the hypotenuse
2.
AD CD

3. CD DB
2. Altitude of rt. Δ to hypotenuse
divides into 2 ~ Δs
3.
Similarity in Right Triangles
Find the values of x and y in the following right triangle.
You Try One!!!
Find the values of x and y in the following right triangle.
Kick it up a notch!
Find the value of x in the following right triangle.
2x - 1
1
x
Real World Connection
As Marla arrives at the lake from the parking lot, she reads a sign
that says she is 320m from the dock. How far is Marla from the
information center?
“You wasted $150,000 on an education you coulda
got for $1.50 in late fees at the public library.”
7.4 Similarity in Right Triangles
HW 7.4: #1-21, 34, 35, 50, 51