Unit 6 (Part II) – Triangle Similarity



Cholkar MCHS MATH II ___/___/___ Name____________________________

|5.2 |What can we discover about the perpendicular bisectors in a triangle? |

| |What is the relationship between a point on an angle bisector and the sides of the angle? |

|Do Now |Find the values of the variables in the diagrams below: |

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| |a. b. c. |

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NOTES:

|PERPENDICULAR BISECTOR THEOREM: |

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Will the converse of this statement be true?

|CONVERSE OF THE PERPENDICULAR BISECTOR THEOREM: |

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1. [pic] is the perpendicular bisector of [pic]. Find AD.

2. [pic] is the perpendicular bisector of [pic].

a. Which segments are congruent?

b. Is V on [pic]? Explain.

3. Write a proof for the problem below. (about 8 steps)

Given: [pic] is the perpendicular bisector of [pic]

Prove: [pic]

An ______________ ________________ divides an angle into two congruent angles.

|ANGLE BISECTOR THEOREM: |

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Is the converse of the angle bisector theorem true?

|CONVERSE OF THE ANGLE BISECTOR THEOREM: |

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Let’s see if we can prove the Angle Bisector Theorem.

Given: [pic] bisects [pic]

[pic]

[pic]

Prove: [pic]

EXTRA CLASSWORK EXAMPLES:

1. [pic] is the perpendicular bisector of [pic]. Find AD.

2. Find the value of x in each diagram below.

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|[pic] |[pic] |[pic] |

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d. Can you conclude that [pic] bisects [pic]? Explain. e. Is [pic]? Explain.

Cholkar MCHS MATH II ___/___/___ Name____________________________

HW #

|1. In the diagram, [pic] is the perpendicular bisector of [pic]. Find |If [pic] is the perpendicular bisector of [pic], what is the value of AB? |

|[pic]. |(Find x first.) |

|[pic] |[pic] |

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|If [pic] and [pic], what is the length of LM? |Draw point Q anywhere on [pic]. If [pic], what is the length of MQ? |

|[pic] |[pic] |

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|5. |6. |

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|7. Find the value of x. |8. Find the value of x. |

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REVIEW:

9. Find the value of x and classify the triangle by its angles.

10. Find the measure of angles D, E, and F.

11. In [pic], [pic], [pic], and [pic]. What type of triangle is [pic]? Explain your reasoning.

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[pic]

[pic]

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