Friday, March 16, 2007
Geometry (Class 59)
Overview
Today we continue to develop understanding of how the ratios of the sides of right triangles can be used to find missing sides and angles. We develop a table of ratios based on triangles that the class constructs. In our warm-up we discuss the concept of Pythagorean Triples (http://en.wikipedia.org/wiki/Pythagorean_triple). We also take Quiz 9.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios
§9.2 (Txt. p.535) The Pythagorean Theorem
§9.3 (Txt. p.543) The Converse of the Pythagorean Theorem
Key Attitudes
Mathematics is about justification.
Key Ideas
If two right triangles have one additional congruent pair of angles, then the triangles are similar.
If two right triangles are similar, then the ratios of their sides are equal.
If you know the measure of one non-right angle in a right triangle and the length of one side, then you can find the lengths of the other sides and the measures of the other angles.
If you know the length of two sides of a right triangle, then you can find the lengths of all of the sides of the right triangle.
If the square of the longest side of a triangle is equal to the sums of the squares of the lengths of the two short sides of the triangle, then the triangle is a right triangle.
If the square of the longest side of a triangle is greater than the sums of the squares of the lengths of the two short sides of the triangle, then the triangle is an obtuse triangle.
If the square of the longest side of a triangle is less than the sums of the squares of the lengths of the two short sides of the triangle, then the triangle is an acute triangle.
To simplify a square root, you factor out the largest perfect square and take its square root, then write the result as a product.
Key Skills
Using trigonometric ratios to solve right triangles.
Writing and solving proportions.
Determine if a triangle is right, acute, or obtuse when given the lengths of the sides.
Simplifying square roots
Vocabulary
Pythagorean Triple
Converse of the Pythagorean Theorem
Trigonometric Ratios
Reference Angle
Handouts
No Handouts Posted
Assignment
§9.1 (Txt. p.531)#21, 22, 25, 26, 28, 35
§9.2 (Txt. p.538) #7-9, 16, 17, 25
Finish drawing, measuring, and calculating the trigonometric ratios for the triangle you were assigned.
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.
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