Transcript LESSON 8.4: Similar Polygons

LESSON 8.4: Similarity in
Right Triangles
OBJECTIVES:
To determine and use relationships in
similar right triangles
Vocabulary and Key Concepts
The geometric mean of two
positive numbers a and b is
________________________
the
positive number m such that
a
m
Example: Find the geometric mean of 4 & 16.
=
____.
m b
If
4 =m
m 16
, then
m 2 = (4)(16)
m 2 = 64
m=8
Thus, the geometric mean of 4 and 16 is 8.
SV
FINDING THE GEOMETRIC MEAN
Find the geometric mean of 3 and 12.
3 =m
m 12
m2 = 36
SV
m =6
NOTE: We use only the positive square root, since
length/distance is measured in positive numbers.
Theorem 8-3: The altitude (perpendicular
segment) to the hypotenuse of a right triangle
divides the triangle into two triangles that
___________________________________
are similar to the original triangle and to
___________________________________
each other
___________________________________.
Corollary 1 to 8-3: The length of the
altitude to the hypotenuse of a right
the geometric mean of the
triangle is ________________________
lengths of the segments of the
________________________________
hypotenuse.
________________________________.
Corollary 2 to 8-3: The altitude to the
hypotenuse of a right triangle
________________________________
separates the hypotenuse so that the
________________________________
length of each leg of a triangle is the
________________________________
geometric mean of the length of the
________________________________
adjacent hypotenuse segment and the
________________________________.
length of the hypotenuse.
FINDING DISTANCE
At a golf course, Maria Teehawk
drover her ball 192 yards straight
toward the cup. Her brother,
G.O. Teehawk drove his ball 240
yard, but not toward the cup. The
diagram shows the results. Find
x and y, their remaining
distances from the cup.
Next, find the distance between
Maria’s ball and G.0.’s ball.
Work Space:
Final Checks for Understanding
1.
How can we use relationships in similar
right triangles in real-life?
2. What is the geometric mean of two
numbers?
3. Find the geometric mean of 15 and 20.
4. Why do we use only the positive square
root when finding the geometric mean
of two numbers?
Homework Assignment: