MATHCP Geometry  - Unit 4: Properties of Equality
Real Number Properties of Equality

For the first nine problems, refer to the chart of Real Number Properties of Equality in the unit area, and then state the property that matches the description.

1) Given three quantities, if the first quantity equals the second quantity, and the second quantity equals the third quantity, then the first quantity equals the third quantity.

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2) Every real number is equal to itself.

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3) If a number equals a second number, then that second number equals the number.

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4) If there are two equal quantities and the same number is subtracted from both of them, then the resulting quantities will be equal.

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5) If two expressions are equal, then one of them may be substituted for the other.

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6) Given three numbers, the result of multiplying the one number by the sum of the other two is the same as multiplying one number by each of the other two, and then adding them.

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7) If there are two equal quantities and the same number is multiplied times both of the quantities, then the resulting quantities will be equal.

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8) If there are two equal quantities and the same number is added to both of them, then the resulting quantities will be equal.

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9) If there are two equal quantities and the same number is divided into both of them, then the resulting quantities will be equal.

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For the next nine problems, select the property of equality that verifies the statement.

10) Which property verifies the statement?

11) Which property verifies the statement?

12) Which property verifies the statement?

13) Which property verifies the statement?

14) Which property verifies the statement?

15) Which property verifies the statement?

16) Which property verifies the statement?

17) Which property verifies the statement?

18) Which property verifies the statement?

The process of solving an equation is shown below. Each step of the process can be verified with a “property of equality”. Copy the proof below on paper or print the picture (right-click, print picture), and then fill in the reasons. Refer to the proof to answer the next four questions.

19) What “property of equality” verifies Statement #2? (In other words, what property was applied to Statement #1 to get Statement #2?)

20) What “property of equality” verifies Statement #3? (In other words, what property was applied to Statement #2 to get Statement #3?)

21) What “property of equality” verifies Statement #4? (In other words, what property was applied to Statement #3 to get Statement #4?)

22) What “property of equality” verifies Statement #5? (In other words, what property was applied to Statement #4 to get Statement #5?)

Reflexive and Symmetric Properties

23) State the “reflexive property”.

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Refer to the figure below to answer the next four questions.

24) Which segment is congruent to segment KL?

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25) Which segment is congruent to segment JM?

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26) Which segment is part of both triangles JKL and JML?

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27) Which segment is marked to show the reflexive property?

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28) In the figure below, what segment illustrates the reflexive property by being a part of both Triangle ABC and Triangle BCD?

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Refer to the figure below to answer the next four questions.

29) Which angle is congruent to angle WVU?

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30) Which angle is congruent to angle TXU?

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31) Which angle is part of both triangles TXU and VWU?

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32) Which angle is marked to show the reflexive property?

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33) In words, describe the symmetric property as it applies to SEGMENTS.

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34) In words, describe the symmetric property as it applies to ANGLES.

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Transitive and Substitution Properties and Informal Proof

35) State the term that matches the following description: A paragraph of statements that explain why a conjecture is true.

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Refer to the transitive property to complete the next two questions.

The next problem is an informal proof of Theorem 4-A and how it applies to SEGMENTS. Fill in the blanks by choosing from the following phrases to complete the proof: “is congruent to”, “is equal to”, “AB”, “CD”, “EF”, “is not congruent to”, and “is not equal to”. Note: All phrases will not be used.

36) Since segment AB is congruent to segment CD, AB __________CD. Since segment CD is congruent to segment EF, EF __________CD. By substitution, AB is equal to __________. By definition of congruence, segment AB __________ segment EF.

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The next problem is an informal proof of Theorem 4-A and how it applies to ANGLES. Fill in the blanks by choosing from the following phrases to complete the proof: “is congruent to”, “is equal to”, “the measurement of angle 1”, “the measurement of angle 2”, “the measurement of angle 3”, “is not congruent to”, and “is not equal to”. Note: All phrases will not be used.

37) Since angle 1 is congruent to angle 2, the measurement of angle 1 __________ the measurement of angle 2. Since angle 2 is congruent to angle 3, the measurement of angle 3 __________ the measurement of angle 2. By substitution, the measurement of angle 1 is equal to __________. By definition of congruence, angle 1 __________ angle 3.

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38) Refer to the figure below to answer the following questions: (a) What is the value of “x”? (b) What is the measure of angle 1? (c) What is the measure of angle 2? (d) What is the measure of angle 3?

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Refer to the figure below to answer the next two questions.

39) Answer the following questions: (a) What is the value of “x”? (b) What is the measure of angle 2? (c) What is the measure of angle 4?

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40) Answer the following questions: (a) What is the value of “y”? (b) What is the measure of angle 1? (c) What is the measure of angle 3?

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