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| For the first three problems, select the term that matches the description. |
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| 1) a line segment that bisects an angle in a triangle and extends from the angle’s vertex to the opposite side |
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| 2) a line segment that connects a vertex of a triangle with the midpoint of the opposite side |
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| 3) a line segment that extends from a vertex of a triangle to its opposite side and is perpendicular to the side |
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| 4) Refer to the figure below to answer the following questions: (a) Name an angle bisector. (b) Name an altitude. (c) Name a median. |
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| Notice in the triangle below that segment KJ, one of the three altitudes of triangle KLM, lies in the exterior of the triangle. Print out or copy the triangle and construct the other two altitudes of the triangle. Name one altitude, segment MN, and the other altitude, segment LP, and then answer the next two questions. |
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| 5)
True or False? Segment MN is an altitude that lies in the exterior of triangle KLM. |
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| 6)
True or False? Segment LP is an altitude that lies in the exterior of triangle KLM. |
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| 7) In the figure below, three medians (segments BF, AE, and CD) are displayed. Which of the following statements is NOT true about the figure? |
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| Print out or copy triangle TRS with vertices of T(–4, –1), R(1,4) and S(3, –5) to answer the next two questions. |
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| Remember, refer to the updated list of theorems, postulates, and definitions that are posted in this unit as you work through the proofs in the following exercises. |
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| 10) Write a paragraph proof or a two-column proof (attach the file) to prove that when given an isosceles triangle, the median to the base of the triangle bisects the vertex angle. |
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| Refer to the figure below to answer the next five questions. The questions are a discussion of proving that segment BD is perpendicular to segment AC given that angles 1 and 2 are congruent, segments DA and DC are congruent, and segment BD bisects angle ADC. |
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| 11) Angles BAD and BCD are congruent. What reasons can we give for making this statement? |
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| 12) We can state that angle ADB is congruent to angle CDB for what reason? |
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| 14) We can also observe that angles ABD and CBD are a linear pair. Knowing that these two angles are congruent and are also a linear pair, what are the measures of these angles? |
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| 15) Have we proven that segment BD is perpendicular to segment AC? Please explain. |
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| 16) For the information and figure shown below, write a paragraph proof or a two-column proof (attach the file) to prove that triangle MNP is congruent to triangle ONP. |
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| Print out or copy the given information and figure shown below. Mark all congruent angles and sides. Label the angles with the given information, and then solve the next eight problems. |
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| 17) Based on the given information, which of the following statements is true about triangle XWZ? |
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| 18) Which equation could be used to solve for “x”? |
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| 20) Calculate the measures of the following angles: (a) angle WXZ (b) angle WXY (c) angle YXZ (d) angle XYZ. |
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| 21) Calculate the measures of the following angles: (a) angle XWZ (b) angle ZWY (c) angle WYX (d) angle XWY. |
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| 22) Which statement of congruence is NOT correct? |
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| 23)
Write a paragraph proof to prove that triangles XYW and ZYW are congruent. |
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| 24) True or False? Triangles XYW and ZYW are congruent ISOSCELES triangles. |
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| 26) Write a paragraph proof of the following statement. |
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| 27) Write a paragraph proof for the following statement. |
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| 28) Write a paragraph proof to prove that triangle GBE is an isosceles triangle. |
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| Fill in the blank for the next three problems. |
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| The next three problems are about the general steps of an indirect proof. Fill in the blanks, as needed. |
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| 35) What assumption could be made to start an indirect proof based on the statement shown below? |
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| 36) What assumption could be made to start an indirect proof based on the statement shown below? |
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| 37) What assumption could be made to start an indirect proof based on the following statement: Angle 1 is complementary to angle 2. |
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| 38) What assumption could be made to start an indirect proof based on the statement shown below? |
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| 39) What assumption could be made to start an indirect proof based on the statement shown below? |
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| In the next five questions, you will be asked about the steps in proving “indirectly” that angle LMP is NOT congruent to angle NMP based on the given information and figure shown below. |
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| 40) What statement can be made to begin an indirect proof of the hypothesis? |
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| Since segment LP is given as NOT congruent to segment PN, proceed on to show that triangles MPL and MPN ARE congruent (a contradiction of CPCTC). |
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| 42) Using the assumptions and rationale demonstrated in the previous two problems and the given information that segment ML is congruent to segment MN, it can be stated that triangles MPL and MPN are congruent based on what postulate or theorem? |
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| 43) If the two triangles, MPL and MPN, are congruent, then segment LP would be congruent to PN by CPCTC. What is wrong with this statement? |
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| 44) So, what must the conclusion be? |
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| 45) Think of a non-math scenario where an indirect proof may be applied. For an example, read the “court room” scenario in the link to “Indirect Proofs”. |
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| Extended Research: Check with your instructor to see if he/she is interested in awarding extra credit to you for writing a one-page report on the following research topic: In quilting there are basic designs that are fundamental in making beautiful quilts. Research the Internet for quilt designs and find a design that is based on congruent triangles. Make a one page report of the type of geometric design that you discovered. You may include information about famous quilters, quilting events, history of quilting, how designs are developed, and/or general information about quilting. You may also include pictures in the report. Include a list of websites that you used as references. Send the document to your instructor via VLA email. |
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| 46) 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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