Pythagorean Theorem

Is it a right triangle? AKA Converse

100

What is the defining characteristic of a right triangle?

one angle is always a right angle (90 degrees); the sides of the triangle satisfy the Pythagorean theorem; and the hypotenuse is the longest side.

200

How can you determine if a triangle is a right triangle without measuring angles?

The square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

300

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle? Why or why not?

YES. 3^{2 +} 4² = 5² or 9 + 16 = 25

400

Using the Pythagorean Theorem, determine if a triangle with sides 6, 8, and 10 is a right triangle.

6² + 8² = 10², or 36 + 64 = 100

500

Determine whether the triangle with side lengths 7, 24, and 25 units forms a right triangle.

7²+24^{2 =} 25², 49+576=625

What is the diagonal?

100

What is the diagonal of a cube with side length 5 units?

8.66, 8.7 units

200

Calculate the length of the diagonal of a rectangular prism with length of 9 units, width of 6 units and height of 12 units.

16.155, 16.2

300

What is the diagonal of a rectangular prism with width of 3 units, length of 8 units and a height of 2 units?

8.77, 8.8

400

What is the diagonal of a cube with sides of 10 inches?

17.32, 17.3

500

What is the diagonal of a rectangular prism with a height of 5 yards, width of 2 yards and length of 7 yards?

8.83, 8.8

Missing side

100

In a right triangle with legs of length 4 and 3 units, what is the length of the hypotenuse?

5

200

Given a right triangle with hypotenuse 17 units and one leg 8 units, find the length of the other leg.

18.79 units

300

A right triangle has one leg of length 5 units and a hypotenuse of 13 units. Determine the length of the other leg.

13.93 units

400

Calculate the missing side length of a right triangle with legs of 9 units and 12 units.

15 units

500

In a right triangle with sides of length 6, 8, and x units, solve for x.

10 units

Distance

100

Find the distance between points (3, 4) and (7, 1).

5 units

200

Determine the distance between points (-2, -1) and (5, 3).

8.06 or 8.1

300

If two points are located at (0, 0) and (10, 15), what is the distance between them?

18.027 or 18.03, or 18

400

Calculate the distance between points (-3, 2) and (4, -5).

9.899, 9.9

500

Find the distance between points (6, -1) and (-4, 5).

11.66, 11.7

Real World Problems

100

 A ladder is leaning against a wall, creating a right triangle. If the ladder is 15 feet long and the base is 9 feet, how high up the wall does the ladder reach?

a²+9²=15^2,  a=12

200

A plane travels 500 miles due east and then 300 miles due north. What is the straight-line distance from the starting point to the final destination?

583.095. 583.1

300

An athlete runs 400 meters east and then 300 meters north. What is the distance back to the starting point?

500 meters

400

A flagpole stands vertically.  A student holds the attached to the top of the flagpole at a distance of 15 meters away from the pole, and the rope is 17 meters long, find the height of the pole.

8 ft.

500

 You’re playing in a baseball game, and you’re stationed at first base. The opposing team’s runner is sprinting toward third base. To throw them out, you need to make a precise throw from first base to third base. How far do you have to throw the ball to reach third base and tag the runner?

• The baseball diamond is a square, with each side measuring 90 feet/
• You’re standing at first base.
• You want to throw the ball directly to third base.

You need to throw the ball approximately 127.28 feet from first base to third base to tag the runner out!