MATH Integrated Math II  - Unit 9: Mid-Semester Review
Points, Lines, Planes

Refer to the figure below to answer the first five questions.

1) Name a plane.

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2) Name three points that are coplanar but do not lie in plane BED.

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3) Name a point that is not coplanar with points B, E, and D.

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4) Name a point that is not coplanar with points A, E, and D.

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5) Name a line segment that lies in plane Q.

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Angles

6) Print out the angle below, and then use a compass to bisect the angle. Name the bisecting ray, ray GT. List the steps you followed to make the construction.

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7) True or False. Angles CGT and DGT (in the previous problem) are congruent.

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

8) Name a linear pair of angles.

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9) Name a pair of obtuse vertical angles.

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10) Name two rays that are perpendicular to each other.

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11) Name a segment.

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12) Name two lines.

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13) Name three points that are collinear.

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14) Name a point that lies in the interior of angle DOB.

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15) Name all points, specified in the figure, that lie in the exterior of angle DOB.

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16) Complete the statement shown below and also state the number of the postulate that supports this assumption.

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17) What is the measure of angle BHC shown in the figure below?

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18) Refer to the figure below to answer the following questions: (a) What kind of angles are angles TUP and PUZ? (b) What equation may be used to solve for “x”? (c) What is the value of “x”? (d) What is the measure of angle PUT? (e) What is the measure of angle ZUP?

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19) Complete the following statement about the previous problem: Since the angles are ______________ angles, the solution can be checked by adding the measures of the angles to see if the sum is ______________ degrees.

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The Coordinate Plane and Line Segments

Refer to the coordinate plane below to answer the next two questions. Each space in the grid represents one unit. Name all specified points and their ordered pairs for the given criteria.

20) Answer the following: (a) Name the points that lie on the x-axis. (b) Name the points that lie on the y-axis.

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21) Answer the following: (a) Name the points that lie in Quadrant I. (b) Name the points that lie in Quadrant II. (c) Name the points that lie in Quadrant III. (d) Name the points that lie in Quadrant IV.

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22) Print out the segment below and draw a point M on segment CH that represents the midpoint of the segment. What is true about segments CM and MH?

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

23) Name the point that is the midpoint of segment GH.

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24) What is the length of segment GB?

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25) What segment completes the statement below and what is the number of the postulate that supports the statement.

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Logic

26) The four building blocks in geometry are UNDEFINED TERMS, DEFINED TERMS, POSTULATES, and THEOREMS. In the statements below, fill in the blanks with one of the four building blocks just mentioned. State the letter of the statement, and then state the answer.

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27) Name three geometric figures that are undefined geometric terms; but, they are accepted to be true and exist.

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28) What is the difference between a postulate and a theorem?

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Use the following statement to answer the next three questions: “If Logan is the daughter of Shari, then Sharon is Logan’s grandmother.” (Assume that Logan is the naturally born daughter of Shari and Shari is the naturally born daughter of Sharon.)

29) Write the converse of the statement, and then state whether it is true or false. If false, give a counterexample.

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30) Write the inverse of the statement, and then state whether it is true or false. If false, give a counterexample.

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31) Write the contrapositive of the statement, and then state whether it is true or false. If false, give a counterexample.

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Properties of Equality

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

32) Which property verifies the statement?

33) Which property verifies the statement?

34) Which property verifies the statement?

35) Select the property of equality that verifies the step shown.

36) Select the property of equality that verifies the step shown.

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

37) What property justifies statement #2?

38) What property justifies statement #3?

39) What property justifies statement #4?

Properties and Proofs of Segments and Angles

40) Copy or print out the partial proof shown below, fill in the blanks, and then answer the following questions: (a) What is the reason for statement #2? (b) What is the reason for statement #3? (c) What is the reason for statement #6?

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Formulas

41) What is the difference between “surface area” and “volume”.

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For the next four problems solve and label the answers correctly.

42) The perimeter of a regular dodecagon is 57.6 cm. How long is one side?

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43) A cube has a volume of 125 cubic inches. (a) What is the length of one edge? (b) What is the surface area of the cube?

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44) Find the volume of a sphere that has a radius of 10 mm. Round the answer to the nearest tenth. (Remember, most computers have a calculator program listed under “Accessories”.)

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45) At what Celsius temperature does water boil? (Hint: Water boils at 212 degrees Fahrenheit.) State the answer and the formula used to solve this problem.

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For the next three problems solve the formula for the given variable.

46) Solve for "h".

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47) Solve for "s".

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48) Solve for "w".

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49) Write a true conditional statement (if-then) based on the Venn diagram.

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