1. Welcome Trig Students. Today’s Agenda 9/7/10: 1. Warm Up 2
Welcome Trig Students! Today’s Agenda 9/7/10: 1. Warm Up 2. Review of Class Syllabus 3. Lecture 4. “Work it out!” 5. Assignment 6. Homework

2. Warm Up
Think back on what you remember about angles and triangles from your previous math classes. Do you remember names of angles? What do you remember about triangles? Write and diagram as much detail as possible!

3. Don’t forget about our class blog!
Ms. Parra’s Amazing Math Blog

4. Notes: Angles Right angle: 90 degrees Straight angle: 180 degrees
Acute angle: less than 90 degree
Obtuse angle: more than 90 but less than 180 degrees
Complementary angles: angles whose sum is equal to 90 degrees
Supplementary angles: angles whose sum is equal to 180 degrees

5. Sample Problems, yay!
Give the complement and supplement of each angle:
1. 40 degrees
degrees
3. Angle “a”

6. Good ol’ Pythagoras!
Pythagoras and his followers, the Pythagoreans established themselves as a secret society around 540 B.C. The Pythagoreans kept no written record of their work; everything was handed down by spoken word. Their influence was not only in mathematics, but also in religion, science, medicine, and music. The British philosopher Bertrand Russell has referred to Pythagoras as “intellectually one of the most important men that ever lived”. Wow, fancy!

7. Pythagorean Theorem
This theorem (or math law) states that in any right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides (called legs). Ummm what does this mean???

8. Don’t worry! What this theorem states is that when given the lengths of 2 sides of a right triangle, you can use the Pythagorean Theorem to find the length of the third side. So…
a2+b2=c2

9. a2+b2=c2
Remember!
The hypotenuse is always the LONGEST side of a triangle!
Check out pg. 5, Figure 5 in your Trig book!

10. Let’s try one together! Pg.6, Figure 7 on Trig book
a= x+7
b= x
c= 13
Set it up!: a2+b2=c2
so…..
(x+7)2+x2= 132
Now, expand and solve!

11. Once we have done all of the math, we realize that we have a quadratic equation (which means you get 2 answers!)
When you set both factors to zero, you get x=5 and x=-12 as solutions.
Is there such thing as a negative length? No, silly! So the only answer that makes sense is the positive answer: x=5

12. A proof of the Pythagorean Theorem
As a student, you must also know how to “prove” the theorem. That means that you have to use other means to get to the final formula:
a2+b2=c2
Begin Lesson on proving theorem on September 9

13. Pg. 5, Figure 6
Let’s use the above figure to prove the theorem. I will set it up on the board, and YOU will prove it!
Knock yourselves out!
P.S. Don’t forget that: (a+b)2=
a2+ 2ab+ b2
That’s the formula for the square of a binomial!

14. You did it!
Remember, being able to prove the Pythagorean Theorem is VERY important, so make sure you KNOW how to do this!! It might come up on a quiz later on….
*wink, wink*

15. “Work it out!” Work out the following problems in your notebook!
Indicate if the angle is acute or obtuse, then find the complement and supplement of each angle.
10o b.50o c. 45o d.90o e. 120o f. 160o
g. X h. y

16. Answer and Diagram:
1. An equilateral triangle is a triangle in which all three sides are equal. What is the measure of each angle in an equilateral triangle?

17. Class work!
Use Pythagorean Theorem to answer problems of page 11 on your Trig book. Don’t worry, we will go over these together! Whatever you do not finish in class will become homework.

18. We <3 Homework
1. Finish all class work that was not completed in class.
2. Everyone MUST go to the class blog and leave a comment with at MINIMUM their first and last name.
3.Return signed syllabus, with ALL signatures including yours and your parents!
4. Review your notes. What’s next? Special Triangles!