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.

I C A N U S E T H E P R O P E RT I E S O F 4 5 4 5 9 0 A N D 3 0 6 0 9 0 T R I A N G L E S .

8.2 - SPECIAL RIGHT 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 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?

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. 3B. 3C. 6D. 6

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. 5B. 10C. 5D. 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 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:PAGE 503, #8 – 20 EVEN, 21,22-26 EVEN,29