Warm-Up

1
Warm-Up
Decide if the segment lengths can form a
triangle. If so, tell whether the triangle is
acute, right, or obtuse.
yes obtuse
yes acute
yes right
4. Find the area of the triangle.
1080 cm2
2
Lesson 7.3 Geometric Mean Right Triangles
The geometric mean of two numbers a and b is the
positive number x such that
Ex) Find the geometric mean between 2 and 10.
3
Theorems
Find x.
4
Practice Find x.
1.
3.
2.
5
y
x
6
2
6
EXAMPLE
Use a geometric mean
B
2. Find BD, BC, and AB
a
c
h
A
C
D
5
8
7
EXAMPLE 3
Find a height using indirect measurement
You use a cardboard square to line up the top and
bottom of the gym wall. Your friend measures the
vertical distance from the ground to your eye and
the distance from you to the gym wall.
Approximate the height of the gym wall.
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EXAMPLE 3
Find a height using indirect measurement
SOLUTION
By Theorem 7.6, you know that 8.5 is the
geometric mean of w and 5.
Write a proportion.
Solve for w.
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Simplifying Radicals
Simplify.
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7.4 Special Right Triangles
A 45- 45- 90 triangle is an isosceles right
triangle.
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EXAMPLE 1
Find the length of the hypotenuse.
SOLUTION
Substitute.
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EXAMPLE 2
Find the length of the hypotenuse.
Substitute.
Product of square roots
6
Simplify.
13
EXAMPLE 3
3. Find the lengths of the legs in the triangle.
SOLUTION
Substitute.
5 x
Simplify.
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for Examples 1, 2, and 3
GUIDED PRACTICE
Find the value of the variable.
15
for Examples 1, 2, and 3
GUIDED PRACTICE
4. Find the leg length of a 45- 45- 90
triangle with a hypotenuse length of 6.
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30- 60- 90 triangles

• In a 30- 60- 90 triangle
• The Short leg is opposite the 30 angle.
• The Long leg is opposite the 60 angle.

60
HYP
Short Leg
30
Long Leg
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Find the length of the missing sides.
4
30
10
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EXAMPLE 1
Find the height of an equilateral triangle
Logo
1. The logo on a recycling bin resembles an
equilateral triangle with side lengths of 6
centimeters. What is the approximate height of
the logo?
SOLUTION
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EXAMPLE 2
2. Find the values of x and y. Write your
answer in simplest radical form.
Substitute.
Multiply fractions.
Simplify.
20
EXAMPLE 2
Substitute and simplify.
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EXAMPLE 3
Find a height
Dump Truck
SOLUTION
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EXAMPLE 3
Find a height
Triangle Theorem
Use a calculator to approximate.
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EXAMPLE 3
Find a height
Substitute.
7 s
Divide each side by 2.
Substitute.
Use a calculator to approximate.
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for Examples 1, 2, and 3
GUIDED PRACTICE
Find the value of the variable.
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Warm-Up
2.