For more information, please see full course syllabus of Pre Algebra

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For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

### Pythagorean Theorem

- A right triangle is a triangle with one right, 90°, angle. It has two legs, which are the shorter sides. The hypotenuse is the longest side and is the diagonal; it‘s the side across from the right angle.
- The Pythagorean Theorem, a
^{2}+ b^{2}= c^{2}, shows how the lengths of the sides in a right triangle are related. The sum of the squares of the legs is equal to the hypotenuse. - The letters a, b, and c are commonly used to represent the sides of a right triangle. a and b are used to represent the legs and c is used to represent the hypotenuse.

### Pythagorean Theorem

Find the length of the hypotenuse of a triangle with legs measuring 6 inches and 8 inches.

- a
^{2}+ b^{2}= c^{2}, where a and b are lengths of the legs and c is the length of the hypotenuse - 6
^{2}+ 8^{2}= c^{2} - 36 + 64 = c
^{2} - 100 = c
^{2} - c = 10

10 inches

Find the length of the hypotenuse of a triangle with legs measuring 16 inches and 30 inches.

- a
^{2}+ b^{2}= c^{2} - 16
^{2}+ 30^{2}= c^{2} - 256 + 900 = c
^{2} - 1156 = c
^{2} - c = 34

34 inches

Find the perimeter of a right triangle with legs of 12 inches and 5 inches.

- a
^{2}+ b^{2}= c^{2} - Perimeter = a + b + c
- 12
^{2}+ 5^{2}= c^{2} - 144 + 25 = c
^{2} - 4169 = c
^{2} - c = 13
- Perimeter = a + b + c =
- 5 + 12 + 13 =

30 inches

Find the perimeter of a right triangle whose legs are length 7 inches and 24 inches.

- a
^{2}+ b^{2}= c^{2} - Perimeter = a + b + c
- 7
^{2}+ 24^{2}= c^{2} - 49 + 576 = c
^{2} - 625 = c
^{2} - c = 25
- Perimeter = a + b + c =
- 7 + 24 + 25 =

56 inches

Determine whether the given lengths can be sides of a right triangle.

15, 17, 8 inches

15, 17, 8 inches

- a
^{2}+ b^{2}= c^{2} - The hypotenuse must be the longest side, so let c = 17
- 8
^{2}+ 15^{2}=^{?}17^{2} - 64 + 225 =
^{?}289 - 289 = 289

Yes

Determine whether the given lengths can be sides of a right triangle.

24, 9, 26 inches

24, 9, 26 inches

- a
^{2}+ b^{2}= c^{2} - The hypotenuse must be the longest side, so let c = 26.
- 9
^{2}+ 24^{2}=^{?}26^{2} - 81 + 576 =
^{?}676 - 657 ≠ 676

No

Dave leans a 41 - inch card against a wall. If the base of the card is 9 inches away from the wall, how high up the wall does the top of the card reach?

- The card, the ground, and the wall form a right triangle, where the card is the hypotenuse
- a
^{2}+ b^{2}= c^{2}

a = 9

c = 41

b = height of wall - 9
^{2}+ b^{2}= 41^{2} - 81 + b
^{2}= 1681 - b
^{2}= 1681 − 81 - b
^{2}= 1600 - b = 40

40 inches

Julie wants to make a fenced area in the shape of a right triangle. One leg of the triangle is 12 feet, and the hypotenuse of the triangle is 15 feet. How long should Julie make the last side of the triangle?

- a
^{2}+ b^{2}= c^{2}

a = 12

c = 15

b = length of last side of triangle - 12
^{2}+ b^{2}= 15^{2} - 144 + b
^{2}= 225 - b
^{2}= 225 − 144 - b
^{2}= 81 - b = 9

9 feet

A Pythagorean Triple is a set of positive integers, a, b, and c, that satisfy the Pythagorean Theorem. Determine whether the following is a Pythagorean Triple.

16, 30, 34

16, 30, 34

- a
^{2}+ b^{2}= c^{2} - 16
^{2}+ 30^{2}=^{?}34^{2} - 256 + 900 =
^{?}1156 - 1156 = 1156

Yes

Determine whether the following is a Pythagorean Triple.

7, 34, 25

7, 34, 25

- a
^{2}+ b^{2}= c^{2} - 7
^{2}+ 25^{2}=^{?}34^{2} - 49 + 625 =
^{?}1156 - 674 ≠ 1156

No

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Pythagorean Theorem

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- What You'll Learn and Why 0:05
- Topics Overview
- Vocabulary 0:36
- Right Triangle
- Legs
- Hypotenuse
- Pythagorean Theorem 1:11
- Arithmetic Example
- Algebra Example
- Find the Length of the Hypotenuse 3:04
- Example 1: Hypotenuse of a Triangle
- Example 2: Hypotenuse of a Triangle
- Find the Length of the Hypotenuse 6:18
- Example 3: Hypotenuse of a Right Triangle
- Extra Example 1: Square Roots 8:41
- Extra Example 2: Perimeter 9:43
- Extra Example 3: Length of Screen 11:58
- Extra Example 4: Length of Wire 13:14

0 answers

Post by Nolan Bohler on April 29, 2014

Just wanted to point out an error here is the practice questions.

Correct me if I'm wrong?

It's in Step 5.(4169 = c2). I did the math here and I came up with "169"

Q. Find the perimeter of a right triangle with legs of 12 inches and 5 inches.

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Step 1. a2 + b2 = c2

Step 2. Perimeter = a + b + c

Step 3. 122 + 52 = c2

Step 4. 144 + 25 = 169 is not (4169)

Step 5. -->4169<-- needs to be 169 = c2

Step 6. c = 13

Step 7. Perimeter = a + b + c =

Step 8. 5 + 12 + 13 = 30 inches

0 answers

Post by Kirnvir Kaur on December 29, 2011

very very helpful ,God bless you