8th grade, Module 12; Pythagorean Theorem

square root

A number which, when multiplied by itself, makes a square. .

proof

A proof is a series of steps used to prove the validity of a theorem

theorem

A statement that can be proven

Right Triangle

A triangle that has one right angle (90 degrees) with 2 legs, and one hypotenuse.

right angle

An angle of exactly 90 degrees.

right triangle

An angle that is 90 degrees (It makes a square in the corner).

14.1

Dylan has a square piece of metal that measures 10 inches on each side. He cuts the metal along the diagonal, forming two right triangles. What is the length of the hypotenuse of each right triangle to the nearest tenth of an inch?

leg

Either of the two shortest sides of a right triangle, they meet at a common vertex to form a right angle.

3.16

If side a = 1 inch and side b = 3 inches, what does side c equal?

14.96

If side a = 10 feet and side c = 18 feet, what does side b equal?

18.02

If side a = 10 meters and side b = 15 meters, how many meters long is side c?

23.43

If side a = 18 inches and side b = 15 inches, what does side c equal?

4.58

If side a = 2 inches and side c = 5 inches, what does side b equal?

10.58

If side a = 3 inches and side c = 11 inches, what does side b equal?

7.21

If side a = 4 feet and side b = 6 feet, what does side c equal?

10.63

If side a = 7 inches, side b = 8 inches, what does side c equal?

9.0

If side b = 12 inches and side c = 15 inches, what does side a equal?

5.74

If side b = 4 feet and side c = 7 feet, what does side a equal?

8.66

If side b = 5 inches and side c = 10 inches, what does side a equal?

converse of the pythagorean theorem

If the lengths of the three sides of a triangle satisfy the Pythagorean equation, then the triangle is a right triangle.

A theorem attributed to Pythagoras that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Pythagorean Theorem

75.4

The diagonal of a rectangular big-screen TV measures 152cm. The length measures 132cm. What is the height of the screen?

hypotenuse

The longest side of a right triangle. It is always opposite of, and never is a part of, the right angle.

square

The result of multiplying a number by itself.

Pythagorean Theorem

Used to find the missing side of a right triangle.

8.9

a=4, b = 8, c=?

11.5

a=?, b=8, c=14

Distance formula

c=

the longest side of a right triangle (C)

hypotenuse

5.0

if side a = 3inches and side b = 4 inches, what does side c equal?

converse

is created when the if-then parts of that theorem are exchanged.