Deductive versus Inductive Reasoning
Similar Triangles
The Greeks
|Objectives: | |
|Calculate the lengths of sides of similar triangles. | |
|Solve word problems involving similar triangles. | |
|Use the two column proof method to prove a geometric result | |
|Vocabulary: | |Formulas: |
|similar triangles | |Proportions of similar triangles: |
| | |[pic] [pic] |
Possible Classroom Examples:
Given that the triangles are similar, find the lengths of the missing sides.
[pic] [pic]
Given that the triangles are similar, find the lengths of the missing sides.
[pic] [pic]
A 5.4-foot –tall woman casts a shadow of 2 feet at the same instant that a telephone pole casts a shadow of 9 feet. How tall is the telephone pole?
Find the length of the longest object that will fit inside a cube 2 feet long, 2 feet wide, and 2 feet high.
Use the two-column method to prove the result
Given: [pic]
[pic]
Prove: [pic]
Use the two-column method to prove the result
Given: [pic]
[pic]
Prove: [pic]
A circle is inscribed in a square. Find the ratio of the area of the circle to the area of the square.
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[pic]
[pic]
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