Monday, March 03, 2008
Geometry (Class 57)
Announcements
Test Friday. Focus will be on Chapter 8 Lesson 1- Lesson 5.
Lesson Title
Some Surprising Relations 2
Overview
In the last class we saw how two transversals cut three parallel lines into sections with equal ratios. In today’s class we see how the angle bisector of one angle in a triangle also creates proportions.
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 (#56)
§8.6 (Txt. p.502) #11, 12, 15, 16, 21-24, 34, 40
Finish Proof 1 for Chapter 8: Lesson 4- Some Surprising Relations
Handouts
Chapter 12- Lesson 1: Solid 1
Chapter 8- Lesson 5: Donald Duck in Mathmagic Land
Assignment
Complete Warm-Up
§8.6 (Txt. p.502) #25-28, 39a-c
Txt. p.517 #8-17
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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