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1) Define a two-column proof. |
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Now you will take an in-depth look at the proof for Theorem 7-B. Study the proof for Theorem 7-A found in the unit link to “Addition Properties”. The proof for Theorem 7-A will serve as a good model for completing the proof of Theorem 7-B below. First, copy or print the partially completed proof, complete the proof, and then answer the next five questions. |
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Select the reasons from the following list: “Substitution Property of Equality”, “Definition of Congruence”, Angle Addition (Postulate 2-B)”, “Addition Property of Equality”. Some reasons may be used more than once. |
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9) Now that you have completed the proof of Theorem 7-B, briefly explain the main idea of this theorem in your own words. |
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Copy or print the next partially completed proof, complete the proof, and then answer the next six questions. |
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10) What is the statement in step #1? |
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16) Now that you have completed the proof of Theorem 7-C, briefly explain the main idea of this theorem in your own words. |
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17) Read and study Theorem 7-G, and then briefly explain the main idea of this theorem in your own words. |
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Refer to the figure below to answer the next two questions. |
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18) What information is given? (Hint: Make statements regarding the segments that are marked with “hash marks”.) |
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19) If segment AD is subtracted from segment AB and segment CE is subtracted from segment CB, what is true about segment BD and BE. |
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20) Read and study Theorem 7-H, and then briefly explain the main idea of this theorem in your own words. |
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Multiplication and Division Properties |
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21) Which of the terms mean to divide a geometric shape into three equal parts? |
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22) Which of the terms mean to divide a geometric shape into two equal parts? |
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Draw a diagram to represent the following geometric figure, and then answer the next six questions: On Segment KN, points L and M are collinear with K and N and fall between points K and N. Point L is closer to point K than point M. Points L and M trisect segment KN. |
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29) Select the term that fills in the blank in the following statement: If point P is placed as a midpoint between points L and M, then point P _____________ segment LM. |
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Draw a diagram to represent the following geometric figure, and then answer the next two questions: Angle TOV is an obtuse angle that measures 145 degrees. Ray OM bisects angle TOV. |
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A good definition is reversible. For the next two problems, good definitions are given. Read the definition, and then complete the reverse of the definition. |
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34) Examine this poorly constructed definition: “Complementary angles total 90 degrees”. Rephrase the definition so that it is reversible. (a) Write the new definition and (b) write its reverse. |
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35) Write a proof for the given information and the conclusion. You may write the proof in paragraph form or you can write a formal proof using statements and reasons. If you decide to write a formal proof, you may complete the proof in a word-processing document and attach it below. |
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36) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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