Upcoming SlideShare
×

# Pythagorean slide

3,827 views
3,289 views

Published on

Published in: Education
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
3,827
On SlideShare
0
From Embeds
0
Number of Embeds
5
Actions
Shares
0
39
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Pythagorean slide

1. 1. CSO: M.O.8.4.3<br />Objective:<br />Students will solve right triangle problems where the existence of triangles is not obvious using the Pythagorean Theorem. <br />
2. 2. Legs – The sides that form the Right (90⁰) angle.<br />Hypotenuse – The side opposite the right angle, it is the longest side of the triangle.<br />Converse – reversing the parts.<br />Helpful Vocabulary<br />
3. 3. Pythagorean Theorem<br />Describes the relationship between the lengths of the legs and the hypotenuse for any right triangle<br />Hypotenuse<br />Leg 1<br />Leg 2<br />
4. 4. IN WORDS AND SYMBOLS<br />In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the length <br />c2 = a2 + b2<br />
5. 5. Who is Pythagoras?<br />
6. 6. Born in Samos (Island in Aegean Sea)Around 570 - 495 BC<br />
7. 7. Greek Philosopher, mathematician, and Mystic<br />
8. 8.
9. 9. Proofs<br />First Video Proof<br />Second Video Proof<br />Third Video Proof<br />
10. 10. Historical Note<br />While we call it Pythagoras‘ Theorem, it was also<br />known by Indian, Greek, Chinese and babylonian mathematicians well before he lived ! <br />
11. 11. Using a Centimeter Grid to find area<br />Area = 1 cm<br />Area = 16 cm squared<br />Area = 48 cm squared<br />
12. 12. 3-4-5 Rule<br />This rule is used to check for the existence of a Right corner.<br />Simply Stated:<br />The measure of any side of 3 units, plus the next side of 4 units has to have a diagonal side of 5 units. <br />
13. 13. 3-4-5 Rule Expanded<br />This is the 3-4-5 Rule<br />3 squared is 9<br />4 squared is 16<br />9+16 = 25<br />Square Root of 25 is 5<br />Make a Conjecture<br />If the length of one side is 6 and<br />Length of the next side is 8,<br />What would be the length of the longest side if this was a Right Triangle and 6 and 8 were the two shorter sides?<br />10<br />
14. 14. The answer is 15 since we will not have a negative side to the triangle<br />
15. 15. Now let’s try a problem together<br />
16. 16. c<br />Side a =12 ft<br />Side b = 18 ft<br />Find the length of the hypotenuse of the above Right Triangle? <br />