Monday, March 31 st True or False 1. All congruent Triangles are similar Triangles 2. All rectangles have to be similar.

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Monday, March 31 st True or False 1. All congruent Triangles are similar Triangles 2. All rectangles have to be similar

EOCT Week 12 #1

Right Triangles & Trig This Week Monday: Pythagorean Theorem Tuesday: Triangles Wednesdays: Thursday: SOHCAHTOA ratios Friday: QUIZ

Who remembers Pythagorean Theorem?!!

Who is Pythagoras? There are arguments about who actually first proved the Pythagorean Theorem. There is no evidence of whether Pythagoras or one of his students actually developed the theorem. Pythagoras was a mathematician who lived from BC. He was a well known teacher and built a well known school. He allowed all to come to his school including females, which was unusual for his time. His students were placed under a strict code of conduct and thought.

I. Vocabulary ONLY Right Triangles Hypotenuse: O longest side of the triangle OCOC Legs: O Two short sides O A and B

II. Area and the Pythagorean Theorem

Why does it work? O “Square” actually means the SQUARE that is attached to each side O If you know the AREA of TWO sides, you can find all the side lengths!!!!!!!

When finding area of a square you… o Multiply Length x Width OR o Square one side length!

What is the area of the square of the hypotenuse?? 3 ²=9 4 ²= =c² 25=c² Area=√25 Hypotenuse=5

#1

#2 Find all side lengths

III. Finding missing Hypotenuse

Finding the Length of the Hypotenuse Steps: 1. Substitute numbers in for correct variables 2. Simplify 3. Use inverse operations to solve for C

Practice Problems 1. a= 4 b = 3 c=?2. a=2 b=7c=?

IV. Finding missing Side Lengths

Finding the length of a leg Steps: 1. Substitute the numbers in for the correct variables 2. Simplify 3. Use inverse Operations to get variable by itself

Practice Problems 1. c= 20 b=12 a= ?2. a= 3 c= 7 b= ?

IV. Pythagorean Triples

Because……… ²+4²=5² ²+5²=13²

O Example1: a=3, c= 5, so b has to be:________ O Example2: b=12, c=13, so a has to be:________

*Same rule applies to the MULTIPLES of these two sets of numbers; as long as you are multiplying EACH side length by the same number

You Try!

V. Word Problems Steps 1. Draw out the problem (right triangle) 2. Label 2 sides 3. Use pythagorean Theorem to find the third 4. Check answer: Does this make sense?

Example #1

Example #2 A ship is 12 meters from the base of the lighthouse. The lighthouse is 16 meters tall. What is the distance from the front of the ship to the top of the lighthouse?