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Geometric mean
45-45-90 Right Triangles
30-60-90 Right Triangles
Facts
MYSTERY!! (0_0)
100

Find the geometric mean of {5,5}

5

100
If an isosceles right triangle has a hypotenuse of 4√2 then what is the length of one of the legs of that triangle?
4
100
The short leg length is 6 and the long leg length is 6√3. What is the length of the hypotenuse?
12
100

In an Isosceles right triangle what process can you do to find to sides given just the hypotenuese?

Divide the hypotenuese by the square root of two.

100

Daily Double! Can you have an angle bigger than 90 degrees in a right triangle?

No

200

Find the geometric mean. {50, 2}

10

200
What is the ratio of the sides of an Isosceles Right Triangle?
1:1:√2
200
Daily Double! In a 30-60-90 triangle the short leg length is 3. What is the length of the long leg?
3√3
200

Can a triangle be both a 30-60-90 and an isosceles right triangle?

no

200

Can a triangle be both isosceles and right?

yes 45-45-90

300

Find the geometric mean. {2, 32}

8

300
If an isosceles right triangle has a leg length of 5 what is the lengths of the hypotenuse?
5 square root of 2
300
What is the ratio of the sides of a 30-60-90 triangle?
1:2:√3
300

Daily Double! The difference in arithmetic mean and geometric mean.

adding/divide by number in set

multiplying/root by number in set

300

In the Pythagorean theorem, what letter stands for the hypotenuse?

c

400

Find the geometric mean. {2, 4, 8}

64

400
If an isosceles right triangle has a hypotenuse of 6√2 , what is the lengths of both legs?
6
400
The length the short leg is 3√3. What is the length of the hypotenuse?
6√3
400

As a general rule who would use right triangles more, a doctor, an engineer or a corporation owner?

An engineer

400

When using the Pythagoren theorem to solve for the hypotenuse what is the last step?

square root to solve for c (not c^2)

500

Find the geometric mean. {8, 9, 3}

6

500
If a right triangle has side lengths of 4,4 and 4√2 what type of right triangle is it?
45-45-90 Isosceles Right Triangle
500
The length of the long leg is 8√3. What is the length of the hypotenuse?
16√3
500

In a 45-45-90 right triangle, are the legs are always the same length?

Yes

500

Name the 2 special right triangles.

45-45-90

30-60-90