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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 5-B. Study the proof for Theorem 5-A found in the unit link to “Addition Properties”. The proof for Theorem 5-A will serve as a good model for completing the proof of Theorem 5-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 1-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 5-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 5-C, briefly explain the main idea of this theorem in your own words. |
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| 17) Read and study Theorem 5-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 5-H, 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 three questions. |
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| 21) State the angles that are congruent based on “hash marks” shown on the figure. |
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| 22) If angle QRS is subtracted from angle QRT and angle STQ is subtracted from angle STR, what are the names of the two congruent angles that are the result of finding the differences? |
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| 24) Based on the given information and any “subtraction property” theorems, how can you deduce that angle 7 must measure 35 degrees? |
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| Multiplication and Division Properties |
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| 25) Which of the terms mean to divide a geometric shape into three equal parts? |
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| 26) 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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| 33) 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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| 38) 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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| 39) 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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| 40) 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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| 41) 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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| 42) 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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| No offline activities found |
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