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.

Section 6.1 Students will apply the Pythagorean theorem and properties of similar triangles to discover patterns in 30-60-90, 45-45-90 triangles and Pythagorean Triples.

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

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

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

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

Examples

Homework Worksheets Simplifying radicals Rationalizing the denom

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

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

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

Examples

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

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

Examples

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

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

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 30-60-90 Triangles Section 6-3 45-45-90 Triangles

Examples

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

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

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?

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

Example Work through 6-14

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

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

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

Trig Ratios and Special Right Triangles 45-45-90 Sin and cos are the same from both angles because they are 45 Tan is always 1 because of congruent sides 30-60-90 Rationalize the denom Set up proportions to solve

Pythagorean Identity

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