Thursday, February 28, 2008
Geometry (Class 56)
Announcements
Check out the crossword for this chapter’s vocabulary!
Lesson Title
Some Surprising Relations
Overview
The warm-up for today’s class focuses on the relationships between perimeter, area, and volume of similar shapes as well as using logic to solve a puzzle related to distances on a map. The lesson for today focuses on two proportional relationships, one related to triangles and the other to parallel lines. We will investigated, conjecture, and then prove these relationships. As time permits, we will then begin looking more closely at a special type of proportion, the “Geometric Mean”.
Textbook Sections
§8.6 (Txt. p. 498) Proportions and Similar Triangles
Vocabulary
similar, similarity
similarity statement
scale factor
statement of proportionality
Key Attitudes
Math is about thinking creatively.
Key Ideas
Triangles are similar if and only if all of the corresponding sides of the triangles are in equal ratios. (Definition of Similarity)
Triangles are similar if and only if two pairs of angles are congruent. (AA Similarity Theorem and Converse of AA Similarity Theorem)
Triangles are similar if and only if a pair of angles are congruent and both pairs of adjacent sides are in the same ratio (SAS Similarity Thm. and Converse of SAS Similarity Theorem)
If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. (Angle Bisector Proportionality Theorem)
If three parallel lines intersect two transversals, then they divide the transversals proportionally. (Parallel Lines Proportionality Theorem)
Key Skills
Use the Angle Bisector Proportionality Theorem to find missing lengths.
Use the Parallel Lines Proportionality Theorem to find missing lengths.
Turn-In (#55)
Test Corrections
Complete warm-up (Analyzing Proofs from Test 8)
Chapter 8- Lesson 3 Problems
Handouts
Chapter 8- Lesson 4: Some Surprising Relations
Assignment
§8.6 (Txt. p.502) #11, 12, 15, 16, 21-24, 34, 40
Finish the first proof from Chapter 8 Lesson 4
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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