5-8
5-8 Applying
ApplyingSpecial
SpecialRight
RightTriangles
Triangles
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
Holt
Geometry
5-8 Applying Special Right Triangles
Do Now
For Exercises 1 and 2, find the value of x.
Give your answer in simplest radical form.
1.
2.
Simplify each expression.
3.
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4.
5-8 Applying Special Right Triangles
Objectives
TSW justify and apply properties
of 45°-45°-90° triangles.
TSW justify and apply properties
of 30°- 60°- 90° triangles.
Holt Geometry
5-8 Applying Special Right Triangles
A diagonal of a square divides it into two congruent
isosceles right triangles. Since the base angles of an
isosceles triangle are congruent, the measure of
each acute angle is 45°. Another name for an
isosceles right triangle is a 45°-45°-90° triangle.
A 45°-45°-90° triangle is one type of special right
triangle. You can use the Pythagorean Theorem to
find a relationship among the side lengths of a 45°45°-90° triangle.
Holt Geometry
5-8 Applying Special Right Triangles
Holt Geometry
5-8 Applying Special Right Triangles
Example 1: Finding Side Lengths in a 45°- 45º- 90º
Triangle
Find the value of x. Give your
answer in simplest radical form.
Holt Geometry
5-8 Applying Special Right Triangles
Example 2: Finding Side Lengths in a 45º- 45º- 90º
Triangle
Find the value of x. Give your
answer in simplest radical form.
Holt Geometry
5-8 Applying Special Right Triangles
Example 3
Find the value of x. Give your answer in
simplest radical form.
Holt Geometry
5-8 Applying Special Right Triangles
Example 4
Find the value of x. Give your answer in
simplest radical form.
Holt Geometry
5-8 Applying Special Right Triangles
Example 5: Craft Application
Eric is cutting a square of material for a
tablecloth. The table’s diagonal is 36 inches.
He wants the diagonal of the tablecloth to be
an extra 10 inches so it will hang over the
edges of the table. What size square should
Eric cut to make the tablecloth? Round to the
nearest inch.
Holt Geometry
5-8 Applying Special Right Triangles
Example 6: Application
Sarah wants to make a bandana for her dog by folding a
square cloth into a 45°-45°-90° triangle. Her dog’s neck has
a circumference of about 32 cm. The folded bandana needs
to be an extra 16 cm long so Sarah can tie it around her
dog’s neck. What should the side length of the square be?
Round to the nearest centimeter.
Holt Geometry
5-8 Applying Special Right Triangles
Example 7
Caelyn’s dog is wearing a square bandana
with a side length of 42 cm. What would you
expect the circumference of her dog’s neck to
be? Round to the nearest centimeter.
Holt Geometry
5-8 Applying Special Right Triangles
A 30°-60°-90° triangle is another special right
triangle. You can use an equilateral triangle to find
a relationship between its side lengths.
Holt Geometry
5-8 Applying Special Right Triangles
Example 8: Finding Side Lengths in a 30º-60º-90º
Triangle
Find the values of x and y. Give
your answers in simplest
radical form.
Holt Geometry
5-8 Applying Special Right Triangles
Example 9: Finding Side Lengths in a 30º-60º-90º
Triangle
Find the values of x and y. Give your
answers in simplest radical form.
Holt Geometry
5-8 Applying Special Right Triangles
Example 10
Find the values of x and y.
Give your answers in simplest
radical form.
Holt Geometry
5-8 Applying Special Right Triangles
Example 11
Find the values of x and y.
Give your answers in
simplest radical form.
Holt Geometry
5-8 Applying Special Right Triangles
Example 12
Find the values of x and y.
Give your answers in
simplest radical form.
Holt Geometry
5-8 Applying Special Right Triangles
Example 13
Find the values of x and y.
Give your answers in
simplest radical form.
Holt Geometry
5-8 Applying Special Right Triangles
Example 14: Using the 30º-60º-90º Triangle Theorem
An ornamental pin is in the shape of
an equilateral triangle. The length of
each side is 6 centimeters. Josh will
attach the fastener to the back along
AB. Will the fastener fit if it is 4
centimeters long?
Holt Geometry
5-8 Applying Special Right Triangles
Example 15: Application
The frame of the clock shown is an
equilateral triangle. The length of
one side of the frame is 20 cm. Will
the clock fit on a shelf that is 18 cm
below the shelf above it?
Holt Geometry
5-8 Applying Special Right Triangles
Example 16: Application
What if…? A manufacturer wants to
make a larger clock with a height of
30 centimeters. What is the length
of each side of the frame? Round to
the nearest tenth.
Holt Geometry
5-8 Applying Special Right Triangles
Holt Geometry
5-8 Applying Special Right Triangles
Lesson Quiz: Part I
Find the values of the variables. Give your
answers in simplest radical form.
1.
2.
x = 10; y = 20
3.
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4.
5-8 Applying Special Right Triangles
Lesson Quiz: Part II
Find the perimeter and area of each figure.
Give your answers in simplest radical form.
5. a square with diagonal length 20 cm
6. an equilateral triangle with height 24 in.
Holt Geometry