here you go...here's the study guide and the answer key! Enjoy.
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On Monday, we looked at some practical applications of the pythagorean theorem and also considered a challenging problem that required some drawing.
On Friday, we presented the distance formula as another way to write the pythagorean theorem. Students saw that the distance formula can be used to find the distance between two points on a coordinate plane (in addition to creating a right triangle).
Today, we looked at the pythagorean theorem, and saw that we can prove that a triangle is a right angle if a^2+b^2=c^2.
Now that we know more about irrational numbers, and we already know an algebraic proof of the pythagorean theorem, it is a good time to revisit this proof, and introduce another proof that is geometric in nature and makes use of the concepts of similar triangles.
This lesson had students use brute mathematical force to approximate irrational numbers to the nearest hundredth. It required students to use number sense AND then multiplication.
Students learned in the past how to convert finite decimals to fractions by placing the decimal over the appropriate power of ten, but this lesson showed students how to convert repeating decimals to fractions using equations.
In this lesson, we defined the set of rational and irrational numbers, and found ways to convert fractions into finite decimals (depending on the denominator of the fraction).
We traveled back to our comfort zone for a brief while today by solving equations. The wrinkle is that these equations contained exponents or radical signs.
Today, we looked at square roots and we simplified them by factoring out perfect squares from the radical symbol.
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