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Select the correct answers that complete the statements in the next nine problems. |
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1) The definition of an inequality states that for any real numbers, a and b, a > b if and only if there is a positive number c, such that __________. |
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2) True or False: The comparison property or the inequalities of real numbers is: a < b, a = b, or a > b. |
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3) In the transitive property of the inequalities of real numbers, if a < b, and b < c, then __________ OR if a > b, and b > c, then __________. |
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4) In the addition property of the inequalities of real numbers, if a > b, then a + c ____ b + c OR if a < b, then a + c ____ b + c. |
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5) In the subtraction property of the inequalities of real numbers, if a > b, then a – c ____ b – c OR if a < b, then a – c ____ b – c. |
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6) In the multiplication properties of the inequalities of real numbers, if “c” is positive and a < b, then ac ____ bc OR if “c” is positive and a > b, then ac ____ bc. |
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7) In the multiplication properties of the inequalities of real numbers, if “c” is negative and a < b, then ac ____ bc OR if “c” is negative and a > b, then ac ____ bc. |
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8) In the division properties of the inequalities of real numbers, if “c” is positive and a < b, then (a/c) ____(b/c) OR if “c” is positive and a > b, then (a/c) ____ (b/c). |
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9) In the division properties of the inequalities of real numbers, if “c” is negative and a < b, then (a/c) ____(b/c) OR if “c” is negative and a > b, then (a/c) ____ (b/c). |
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For the next six problems select the property that justifies the statement. |
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10) Select the property that justifies the statement. |
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11) Select the property that justifies the statement. |
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12) Select the property that justifies the statement. |
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13) Select the property that justifies the statement. |
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14) Select the property that justifies the statement. |
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15) Select the property that justifies the statement. |
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In the next two problems, solve using your knowledge of inequalities. |
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18) Bill is going to purchase a tractor and backhoe attachment for a payment of $625 MONTHLY for 3 years. His goal is to finance, at most, $20,000. Write an inequality comparing ”the amount he must pay back in all” to “$20,000”, and then state whether he has met his goal. |
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4000 character(s) left Your answer is too long. |
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21) A partial “indirect” proof of the Exterior Angle Inequality Theorem is shown in the unit link to “Inequalities”. An incomplete proof of Cases 3 and 4 are shown below. State the number and the corresponding statement or reason of each of the eight missing parts of the proof. |
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4000 character(s) left Your answer is too long. |
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22) Refer to the figure below to answer the following questions. (The figure is drawn to scale.) (a) Which is greater, the measurement of angle 5 or the measurement of angle 3? (b) Which is greater, the measurement of angle 1 or the measurement of angle 5? (c) State one angle greater than angle 3. (d) State one angle that is less than the measure of angle 2. |
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4000 character(s) left Your answer is too long. |
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Triangle Side and Angle Inequalities |
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24) Read the two theorems (13-B and C) in the link to “Triangle Side and Angle Inequalities”, and then select the statement that is NOT true. |
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Refer to triangle RST in the figure below to answer the next two questions. |
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Find the measures of the three angles in triangle LMN based on the information given below, and then answer the next two questions. (Hint: Apply Theorem 10-A.) |
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27) What is (a) the value of “x”, (b) the measure of angle L, (c) the measure of angle M, and (d) the measure of angle N? |
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4000 character(s) left Your answer is too long. |
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28) Select the inequality statement that compares the lengths of the three sides of the triangle from largest to smallest. |
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29) In an obtuse scalene triangle, one angle measures 50 degrees. Which side is this angle opposite? |
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30)
Write a proof for the information and the conclusion given below. You may write the proof in paragraph form or 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. (Hint: You will apply two theorems from the unit, Theorems 13-A and 13-C.) |
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20000 character(s) left Your answer is too long. |
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Attachments |
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32) Copy or print out the partial proof of Theorem 13-D shown below. State the number and the corresponding statement or reason. There are five missing parts of the proof. |
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4000 character(s) left Your answer is too long. |
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Triangle Inequality Theorem |
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34) Will the three segments given below form a triangle? Explain why or why not. |
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4000 character(s) left Your answer is too long. |
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35) Which set of lengths will form a triangle? |
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Two sides of a triangle measure 15 feet and 12 feet in length. Determine several possible lengths of the third side of the triangle, and then answer the next three questions. |
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38) Which inequality describes the range of possible lengths? |
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41) Which side is longer? |
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42) Study the information and figure given below. Which statement is true? |
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43) Please explain how the Hinge Theorem could be used to solve the previous problem. |
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4000 character(s) left Your answer is too long. |
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45) Which angle is greater in size? |
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46) Study the information and figure given below. Which statement is true? |
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47) Please explain how the SSS Inequality Theorem could be used to solve the previous problem. |
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4000 character(s) left Your answer is too long. |
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48)
Write a proof for the information and the conclusion given below. You may write the proof in paragraph form or 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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20000 character(s) left Your answer is too long. |
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Extended Assignment: Check with your instructor to see if he/she is interested in awarding extra credit to you for completing the proof of the given information and figure shown below. If so, type up the formal proof in a word-processing document showing statements and reasons, and then send the proof to your instructor through VLA email. |
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51) 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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