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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