Tuesday, February 26, 2008
Geometry (Class 55)
Chapter 8- Lesson 3: A Triangle in a Triangle (The A-Level proofs and hint cards are at the end.)
Lesson Title
A Triangle in a Triangle 1
Overview
In today’s class our warm-up focuses on the two proofs from the test. For one of the proofs students will need to edit and score “student” work. For the second proof, which had a mistake on the test, students will work to create a proof of their own. We will switch papers and edit each others work as part of the warm-up for the next class.
The lesson for the class continues our work from last Friday where we are examining the relationships created when from a triangle created inside of another triangle by constructing a parallel line.
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 line is parallel to one side of a triangle and intersects the other two sides, then the line divides the two sides proportionally. (Triangle Proportionality, or Side-Splitter, Theorem)
If a line divides two sides of a triangle proportionally, then the line is parallel to the third side of the triangle. (Converse of the Triangle Proportionality, or Side-Splitter, Theorem)
Key Skills
Determine if two triangles are similar using shortcuts (AA, SAS)
Prove triangles similar.
Use the “side-splitter” theorem to solve problems.
Turn-In (#54)
Chapter 8- Lesson 2: Proving Triangles Similar using SAS
§8.5 (Txt. p.492) #13, 14, 26-28, 32, 33
Handouts
Chapter 8- Lesson 3: A Triangle in a Triangle (The A-Level proofs and hint cards are at the end.)
Assignment
Test Corrections
Complete warm-up
Chapter 8- Lesson 3 Problems
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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