Transcript 7.4 Similarity in Right Triangles

7.4 Similarity in Right Triangles
Theorem 7.3
• 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
C
B
D
A
ABC ~ ACD ~ CBD
Vocabulary
• Geometric mean - the number x such that
a x

x b , where a, b and x are positive
numbers
Example
• Find the geometric mean of 4 and 18
Try it
• Find the geometric mean of 3 and 48
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
AD CD

CD DB
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 adjacent
hypotenuse segment and the length of the
hypotenuse
AD AC DB CB

,

AC AB CB AB
Solve for x and y
x
y
5
4
Answer
• Use Corollary 2 to solve for x
4
x

x 45
• Use corollary 1 to solve for y
4 y

y 5
Solve for x and y
4
x
12
y
Answer
• Use Corollary 2 to solve for x
4
x

x 12  4
• Use corollary 1 to solve for y
12 y

y 4
Classwork/Homework
• Pgs 394-395 #2-22 even, 26-36 even