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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