Transcript 7.4 Similarity in Right Triangles

7.4 Similarity in Right Triangles
• The altitude to the hypotenuse of a right triangle
divides the triangle into two triangles that are
similar to the original triangle and to each other.
Geometric Mean
• The geometric mean of two positive numbers a
and b is the positive number x that satisfies
a x
2
 . So, x  ab andx  ab .
x b
Find a Geometric Mean
• Find the geometric mean of 6 and 15.
x  ab
x  6  15
 90  9 10
 3 10
Corollary 1 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.
Corollary 2 to Theorem 7.3
• The altitude to the hypotenuse of a right triangle
separates the hypotenuse so that the length of each
leg of the triangle is the geometric mean of the length
of the hypotenuse and the length of the segment of
the hypotenuse adjacent to the leg.
Using the Corollaries
• What are the values of x and y?
4
x

x 4  12
x  64
2
x  64  8
4 y

y 12
x  48
2
x  48
More Practice!!!!!
• Homework – Textbook p. 464 – 465 #3 –
6, 9 – 21.