WARM UP:
1. What is the length of the hypotenuse of
triangle RST?
2. Cassie’s computer monitor is in the shape of a rectangle.
The screen on the monitor is 11.5 in. high and 18.5 in. wide.
What is the length of the diagonal? Round to the nearest
tenth of an inch.
3. A triangle has side lengths 24, 32, and 42. Is it a right
triangle? Explain.
4. A triangle has side lengths 9, 10, and 12. Is it acute, obtuse,
or right? Explain.
5. Can three segments with lengths 4 cm, 6 cm, and 11 cm be
assessed to form an acute triangle, a right triangle, or an
obtuse triangle? Explain.
8.2 - SPECIAL RIGHT
TRIANGLES
I CAN USE THE PROPERTIES OF 45 45 90 AND
30 60 90 TRIANGLES.
CERTAIN RIGHT TRIANGLES HAVE PROPERTIES
THAT ALLOW YOU TO USE SHORTCUTS TO
DETERMINE SIDE LENGTHS WITHOUT USING THE
PYTHAGOREAN THEOREM.
45 45 90 Triangle Theorem
In a 45 45 90 triangle, both legs are congruent and the
length of the hypotenuse is 2 times the length of a
leg.
PROBLEM: FINDING THE LENGTH OF
THE HYPOTENUSE
• What is the value of each variable?
PROBLEM: FINDING THE LENGTH OF
THE HYPOTENUSE
• What is the length of the hypotenuse of a 45 45 90
triangle with leg length 5 3?
PROBLEM: FINDING THE LENGTH OF
THE HYPOTENUSE
• What is the value of each variable?
PROBLEM:
FINDING THE LENGTH OF A LEG
• What is the value of x?
A. 3
B. 3 2
C. 6
D. 6 2
PROBLEM:
FINDING THE LENGTH OF A LEG
• The length of the hypotenuse of a 45 45 90 triangle
is 10. What is the length of one leg?
PROBLEM:
FINDING THE LENGTH OF A LEG
• What is the value of x?
A. 5 2
B. 10 2
C. 5
D. 10
PROBLEM: FINDING DISTANCE
• A high school softball diamond is a square. The
distance from base to base is 60 ft. To the nearest
foot, how far does a catcher throw the ball from
home plate to second base?
PROBLEM: FINDING DISTANCE
• You plan to build a path along one diagonal of a
100 ft.-by-100 ft. square garden. To the nearest
foot, how long will the path be?
PROBLEM: FINDING DISTANCE
• A courtyard is shaped like a square with 250-ft-long
sides. What is the distance from one corner of the
courtyard to the opposite corner? Round to the
nearest tenth.
ANOTHER TYPE OF SPECIAL RIGHT
TRIANGLE IS A 30 60 90 TRIANGLE.
30 60 90 Triangle Theorem
In a 30 60 90 triangle, the length of the hypotenuse is
twice the length of the shorter leg. The length of the
longer leg is 3 times the length of the shorter leg.
PROBLEM:
USING THE LENGTH OF ONE SIDE
• What is the value of “d” in simplest radical form?
PROBLEM:
USING THE LENGTH OF ONE SIDE
• What is the value of “f” in simplest radical form?
PROBLEM:
USING THE LENGTH OF ONE SIDE
• What is the value of x?
PROBLEM: APPLYING THE 30 60 90
TRIANGLE THEOREM
• An artisan makes pendants in the shape of
equilateral triangles. The height of each pendant is
18 mm. What is the length “s” of each side of a
pendant to the nearest tenth of a millimeter?
PROBLEM: APPLYING THE 30-60-90
TRIANGLE THEOREM
• Suppose the sides of a pendant are 18 mm long.
What is the height of the pendant to the nearest
tenth of a millimeter?
PROBLEM: APPLYING THE 30-60-90
TRIANGLE THEOREM
• What is the height of an equilateral triangle with
sides that are 12 cm long? Round to the nearest
tenth.
AFTER: LESSON CHECK
• What is the value of x? If your answer is not an
integer, express it in simplest radical form.
HOMEWORK:
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