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Name:______________________________________________________________
Date:________________________
Period: ______
Chapter 8: Right Triangles
Topic 5: Mean Proportions & Altitude Rule
Do Now: Use the diagram of similar triangles
and
to complete all parts:
a) Find all three angles in each triangle.
b) Find side ZY.
Geometric Mean
Define “mean” in a plain word: ___________________
Geometric Mean is a little different. Instead of adding and dividing like a regular average… we
________________ and ________________ __________!
Example: The Geometric Mean of 18 and 2 is equal to 6. Let’s explore why:
Exploring Geometric Mean in a Proportion
From the example above:
The “mean” is always equal on both sides of the proportion. The “extreme” values are two different numbers.

In our prior example, 6 was the ______________, 18 and 2 were the _____________________.
Remember how to solve a proportion: ________________ _________________________!!
“The product of the means equals the product of the extremes. “
Examples:
1) Find the geometric mean of 4 and 18 in
2) 25 is the geometric mean of 5 and what
simplest radical form
number?
3)
is the geometric mean of 6 and what number?
Overlapping Triangles Notes
The ___________________ to the ____________________________ of a right triangle
forms two triangles that are similar to each other and to the original
triangle.
Since these triangles are similar, we can establish proportions relating
the corresponding sides and solve for missing pieces of information.
Lets break apart the triangles:
Large Triangle
Left Triangle
The large and left triangles both contain:
1) a right angle <ACB and <ADC
2) <A (Reflexive Property)
Example:
1) Find the value of x.
Practice:
2) Find the value of x.
Right Triangle
Now the left triangle is rotated clockwise.
The left and right both contain:
1) right angles <ADC and <CDB
2) <CAD rotated to <BCD
Steps:
 Separate the triangles
 Set up a proportion to solve
Can you identify a pattern??
ALTITUDE RULE:
Practice:
5) Find the value of x.
6) Find the value of x.
7) Find the value of x.
8) Find the value of x
Name:______________________________________________________________
Date:________________________
Period: ______
Topic 5 Homework: Mean Proportions and Altitude Rule
EVERY QUESTION, EVEN MULTIPLE CHOICE, MUST HAVE SOMETHING SHOWN (WORK OR AN
EXPLANATION) OR NO CREDIT WILL BE GIVEN
1) Find the geometric mean of 3 and 48.
2) Find the geometric mean of 4 and 10 in
simplest radical form.
3)
4) Find the value of x.
is the geometric mean of 12 and
what number?
5) Find the value of x.
7) Find the value of x.
6) Find the value of x.
Review Section:
_____ 8.) In
m<A = 95 and m<B = 50 and m<C = 35. Which expression correctly relates the
lengths of the sides of this triangle?
(1)
(2)
(3)
(4)
_____ 9.) Point P is on line m. What is the total number of planes that are perpendicular to line m and
pass through point P.
(1) 1
(2) 2
(3)0
(4) infinite
_____ 10.) 7, 9, and 10 can be the lengths of the sides of a triangle.
(1) true
(2) false
11.) In the diagram below of trapezoid RSUT, RS||TU, X is the midpoint of RT, and
V is the midpoint of SU. If RS=3x + 7 , XV=3x + 17, and TU = 5x + 11, find the
value of x and the length of all three segments.
12.) The vertex of an isosceles triangle is four times the measure of a base angle. Find the measure of all
three angles of the isosceles triangle.
13.) In two complementary angles, the measure of one angle is 6 more than twice the measure of the other.
Find the measure of both angles.