Pythagorean Theorem
Similar Right Triangles
Special Right Triangles
Pythagorean Inequalities
100
What are the three equations/inequalities for classifying a triangle using the converse of the Pythagorean Theorem?
a2 +b2 = c2 is right a2 + b2 < c2 is obtuse a2 + b2 > c2 is acute
100
The altitude of a right triangle is 18, one segment of the hypotenuse is 12. How long is the hypotenuse?
39
100
The length of the shorter leg of a 30°-60°-90° triangle is 3. What is the length of the hypotenuse?
6
100

The triangle with side lengths 10, 11, and 14 is this type of triangle.

Acute Triangle

200
The length of one leg of a right triangle is 1 and the length of the hypotenuse is the square root of 50. What is the length of the other leg?
7
200
State the equations of both geometric means theorems.
x2 = ab Altitude Th.-the altitude is the geometric mean of the two segments of the hypotenuse. Leg Th.- the leg of the rt. triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
200
The length of the longer leg of a 30°-60°-90° triangle is root108. What is the length of the shorter leg?
6
200

The triangle with side lengths 12, 16, and 20 is this type of triangle.

Right Triangle

300
With side lengths 11.2, 6.5, and 7.1 does this figure form a triangle? If so what type of triangle?
Yes, Obtuse.
300
One leg of a right triangle is x, the hypotenuse is 8 and the segment of the hypotenuse that is not adjacent to the leg x is 2. What is x and what is the length of the altitude? Give your answers in simplest radical form.
x = 4root3 Altitude = 2root3
300
The length of one leg of a 45°-45°-90° triangle is root3. What is the length of the hypotenuse?
root6
300

The triangle with side lengths 15, 20, and 26 is this type of triangle.

Obtuse Triangle

400
What is the value of x when the legs of a right triangle are 2x and 2x + 4, and the hypotenuse is 4x - 4?
x = 6.
400
A right triangle has a hypotenuse 2root89, and legs of 10 and 16. What is the length of the altitude? Round to the nearest tenth.
Altitude = 8.5
400

The long leg of a 30-60-90 triangle is 10. What are the lengths of the short leg and the hypotenuse?

Short leg:  (10sqrt(3)/3) hypotenuse: (20sqrt(3)/3)

400

Verify that the segment lengths form a triangle and if so classify the triangle with side lengths 24, 30, and 6sqrt43.

Obtuse triangle

500
The sides of a triangle are x, x + 4, and 20. The longest side is 20. What values of x make this an acute triangle?
12 < x < 16
500
A right triangle has legs 20 and 15. What is the length of the altitude?
12
500
A 30-60-90 triangle has a longer leg with measure 8. What is the measure of the altitude?
4
500

Verify that the segment lengths form a triangle and if so classify the triangle with side lengths 10, 15, and 5sqrt13.

Right triangle.

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