1. Chapter 6 More Right Triangles
Students will continue to study the similarity and side ratio relationships of right triangles. Students will understand more properties of special right triangles.

2. Section 6.1
Students will apply the Pythagorean theorem and properties of similar triangles to discover patterns in , triangles and Pythagorean Triples.

3. Rationalizing the Denominator
Students will continue to learn about simplifying radicals when in fractional form

4. Review
What is a radical? Square roots or other higher roots How do we write radicals other than square roots? How do we simplify square roots? 1. Prime factor tree 2. Groups of the same number, based on the root 3. 1 number from each group and multiply and put outside 4. Not grouped prime numbers multiply and put inside

5. Rationalize Denominator
When the radical is in the denominator? This is not written correctly We need to get the radical out of the denominator to write it in proper form

6. Process What is the radical in the denominator
Multiple both numerator and denominator by this radical
How do you multiply with radicals
Simplify
Simplify all radicals
Can you divide, simplify fraction

7. Examples

8. Homework
Worksheets Simplifying radicals Rationalizing the denom

9. 6.1.4
Students will recall and apply exponential properties and explore what fractional exponents are.

10. Exponent Properties Review
Multiply
Divide
Negative
Exponent to exponent
Addition and Subtraction
Zero
Distribution

11. Process for Simplifying
Get rid of parenthesis by distributing the exponent
Multiply common bases by adding exponents
Divide common bases by subtracting exponents, always N-D
Write all exponents postive

12. Examples

13. Fractional Exponents and Radicals
These are related How to convert back and forth

14. Examples
Numerator is exponent Denominator is radical Does it matter the order you do it in

15. Examples

16. Homework
Worksheets on Simplifying exponents – pick 6 Fractional Exponents – 4-6 rewrite with radical, 7-9 rewrite with fractional exponent 10, 11, 12, 14 ,15

17. 6.1.1
Special Right Triangles: Students will review and apply special right triangle properties.

18. Review Ideas
Work as a group on 6-1 and 6-2, pg 321 What are the rules you remember about, these have nothing to do with trig ratios Triangles Section Triangles

19. Examples

20. Homework
Finish Face Worksheet using what you just learned Book work 6-3, 6-4 Answers in simplest radical form

21. 6.1.2
Pythagorean Triples: Students will apply previous knowledge to determine patterns or right triangles with integers.

22. Group Work
Work as a group on 6-12, 6-13 Use any method you know to find side lengths, keep answer in simplest radical form What do you notice?

23. Pythagorean triples
This is very helpful with integers, but can this be used with radicals Think of our special right triangles Think of the basic and multiply each side by the same thing What are the main triples 3,4,5 5,12,13

24. Example
Work through 6-14

25. Homework
Book work 6-14 and 6-15 Honors 6-17

26. 6.1.3
Students will apply previous knowledge of Triangle properties and trig ratios to determine patterns and extend their understanding and knowledge.

27. Group work 6-25 Draw the two triangles in your notes
Find all missing sides and angles, sides simplest radical form
Now set up the trig ratios listed, have original and rationalized denom form
What do you notice
This is similar to what the sub talked to you about
6-26 – what do you notice

28. Trig Ratios and Special Right Triangles
Sin and cos are the same from both angles because they are 45 Tan is always 1 because of congruent sides Rationalize the denom Set up proportions to solve

29. Pythagorean Identity

30. Examples
6-27 and 6-28 and 6-30