1. Welcome back from spring break! The rest of the year will FLY by!
Geometry Students…
Welcome back from spring break! The rest of the year will FLY by!
This lesson includes a review of the Pythagorean Theorem. Put the PPT on “play” and take notes on this information. Then read page 417 to page 419 in your text book
Do the homework to the best of your ability.
Then, open PPT 8.2 and check your work.

2. Pythagorean Theorem and its Converse
Chapter 8.1
Pythagorean Theorem and its Converse
Remember that the distance formula is based off of the Pythagorean Theorem.
𝑑= ( 𝑥 2 − 𝑥 1 ) 2 + ( 𝑦 2 − 𝑦 1 ) 2

3. Complete the list of perfect squares:1 2 4 3 9 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

4. Pythagorean Theorem: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
𝑎 2 + 𝑏 2 = 𝑐 2
“c” always represents the _____________________
Hypotenuse – longest side of a right triangle.

5. Pythagorean Triple: a set of nonzero whole numbers a, b and c that satisfy the equation:
In other words, if there are no decimals or fractions for any of the three sides, it is a “triple”
𝑎 2 + 𝑏 2 = 𝑐 2
This triangle is a Pythagorean triple,
Since all sides are whole numbers.

6. Are either of the triangles a Pythagorean Triple?
𝑎 2 + 𝑏 2 = 𝑐 2
Yes! This is a Pythagorean triple! ?
= 13 2
25+144=169
𝑎 2 + 𝑏 2 = 𝑐 2
Yes! This is also a Pythagorean triple! ?
= 17 2
64+225=289

7. Is the triangle a Pythagorean Triple?
𝑎 2 + 𝑏 2 = 𝑐 2
Yes!
= 𝑐 2
= 𝑐 2 20
841= 𝑐 2
841 = 𝑐 2 21
29=𝑐

8. Using simplest radical form:
8 2 + 𝑥 2 = 20 2
64+ 𝑥 2 =400
𝑥 2 =336
𝑥 2 = 336 20
𝑥= 16∙21 8
𝑥=4 21 𝑥
This is NOT a Pythagorean triple.

9. 𝑎 2 + 𝑏 2 = 𝑐 2 ONLY for a right triangle.
How to determine if a triangle is right, acute, or obtuse by its side lengths.
𝑎 2 + 𝑏 2 = 𝑐 2 ONLY for a right triangle.
= 29 2 29
If this is true, then this MUST be a
right triangle. 20 21

10. But what if 𝑎 2 + 𝑏 2 = 𝑐 2 is not true?
First, place all three numbers in the formula: remember “c” is the longest side!
= 31 2 ?
Next square each number. 31
=961 ? 20
841=961 ?
If the hypotenuse is longer, the legs must be widened, meaning it is an obtuse triangle. 21
If the hypotenuse is too short, the legs must be pulled together, meaning it is an acute triangle.

11. Converse of the Pythagorean Theorem: if the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
𝑎 2 + 𝑏 2 = 𝑐 2

12. If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is a an obtuse triangle.
𝑐 2 > 𝑎 2 + 𝑏 2 (obtuse)

13. If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is a an acute triangle.
𝑐 2 < 𝑎 2 + 𝑏 2 (acute)

14. Classify a triangle as right, acute or obtuse:
Side Lengths: 6, 11, and 14
Side Lengths: 7, 8, and 9
Side Lengths: 6, 8, and 10
14 2 __
9 2 __
10 2 __
𝑜𝑏𝑡𝑢𝑠𝑒
𝑎𝑐𝑢𝑡𝑒
𝑟𝑖𝑔ℎ𝑡
𝑐 2 = 𝑎 2 + 𝑏 2 (right)
𝑐 2 < 𝑎 2 + 𝑏 2 (acute)
𝑐 2 > 𝑎 2 + 𝑏 2 (obtuse)

15. Homework – First read page 417-419 in your text book
Homework – First read page in your text book. Page : odd, 18, 21, 24, 25, 32