Questions

1) The diagonals of a rhombus bisect its four angles and are perpendicular.

True

False

2) Compare the definitions of a parallelogram and a kite by stating one similarity and one difference between the two types of quadrilaterals.

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3) A square is NOT which of the following?

a.) rectangle

b.) rhombus

c.) parallelogram

d.) trapezoid

e.) quadrilateral

4) Answer the following questions about kite WXYZ: (a) What is the value of “k”? (b) What is the length of segment WZ?

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5) What is the length of segment EF in the figure shown below based on the given information?

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6) Solve for “y”.

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7) Solve for “x”.

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8) Refer to the figure below to answer the following questions: (a) How many degrees does angle C equal? (b) What is the value of “x”?

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9) In the figure below, “x” represents the distance across the body of water at the specified location. What is the value of “x”?

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10) Study the diagram below to determine the similar triangles. What is the value of “x”?

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11) If ST is a mid-segment of triangle PQR and parallel to segment PQ, what are the coordinates of point S (located on segment PR) and point T (located on QR)?

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12) What is the length of PQ? Round the answer to the nearest tenth. (Hint: Use the distance formula.)

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13) What is the length of ST? Round the answer to the nearest tenth. (Hint: Use the Mid-segment Theorem.)

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14) If the perimeter of triangle ABC is 56, what is the perimeter of triangle XYZ?

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15) Refer to the figure and information shown below to answer the following: (a) Name an angle bisector. (b) Name an altitude. (c) Name a median.

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16) What is the geometric mean between 25 and 75? Round the answer to the nearest tenth.

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17) What is the length of PS in the figure below based on the given information? Round the answer to the nearest tenth.

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18) In the 45-45-90 degree right triangle shown below, what is the length of the hypotenuse? Express the answer to the nearest tenth.

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19) For equilateral triangle QRS shown below, (a) what is the length of one side [x] and (b) what is the length of the altitude [y]? Round the answers to the nearest tenth, if necessary.

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20) What is the (a) sin K, (b) cos K, and (c) tan K? Round each answer to the nearest ten thousandth, if necessary.

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21) What is the size of angle K to the nearest degree? (Hint: Make sure your calculator is in “degree” mode.)

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22) A submarine that is submerged at a depth of 300 meters detects a cruiser at an angle of 54 degrees. What is the direct distance between the submarine and the cruiser? Round the answer to the nearest meter.

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23) An observer on a ship sights a mountain cliff at a 32-degree angle. The cliff is 1250 feet above sea level. How far is the ship from the shore? Round the answer to the nearest foot. (Hint: Draw a picture to help visualize the problem.)

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24) A forest ranger sights a fire from a tower. She is looking down from a tower at a 10-degree angle. The device she uses to locate fires is 100 meters above the ground. How far away is the fire? Round the answer to the nearest meter.

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25) An aircraft 3200 feet above ground begins a two-degree descent when it nears the airport. How many miles (1 mile = 5280 feet) is the aircraft from the airport? Round the answer to the nearest mile. (Hint: Draw a picture to help visualize the problem.)

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26) Use the Law of Sines to solve triangle TUV. (a) What is the measure of angle V? (b) What is the length of TU? (c) What is the length of TV? Round the answers to nearest whole number, when necessary.

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27) Use the law of cosines to solve the triangle. (a) What is the length of NM? (b) What is the measure of angle N? (c) What is the measure of angle M? Round the answers to nearest tenth, when necessary.

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28) Arc JKM is a minor arc.

True

False

29) Arc KM is a minor arc.

True

False

30) Answer the following questions about circle H shown below: (a) What is the measure of arc EF? (b) What is the measure of arc EGF? (c) What is the measure of arc FG?

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31) Suppose you are constructing a circle graph of a survey of 75 persons. The survey results indicate that 18 persons that were surveyed supported the new tax law. What is the size of the angle that would be used to draw the sector of the circle graph that represents the supporters of the new tax law? Round the answer to nearest whole degree.

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32) The measures of chords AC and AB are equal.

True

False

33) If arc AB measures 112 degrees, (a) what is the measure of arc AC and (b) what is the measure of arc BC?

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34) In circle A, if arc XY measures 152 degrees and arc YZ measures 98 degrees, (a) what is the measure of arc XZ and (b) what is the measure of angle XYZ?

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35) In circle E, (a) identify a pair of congruent inscribed angles and (b) name the arc they intercept.

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36) Quadrilateral LMNP is inscribed in circle Q. Arc ML measures 50 degrees and arc LP measures 118 degrees. (a) What is the measure of angle N? (b) What is the measure of angle L? (c) What is the sum of the measures of angles M and P?

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37) In circle S segment QR is a diameter. What is the length of the radius of the circle (SR) if segment PR measures 7 millimeters and PQ measures 24 millimeters?

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38)

In circle C, point D is a point of tangency between tangent AD and radius CD. (a) What is the length of AC? (b) What is the length of BC? (c) What is the length of AB?

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39) In circle L shown below, if arc GH measures 112 degrees and arc JK measures 140 degrees, what is the measure of angle GMH?

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40) Answer the following questions about the figure below: (a) What is the measure of arc BE? (b) What is the measure of arc CD? (c) What is the value of “y”?

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41) In the figure shown below, arc TX measures 125 degrees and arc VX measures 115 degrees. (a) What is the measure of arc TV? (b) What is the measure of angle U?

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42) What is the value of “x”?

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43) Solve for “x”. Round the answer to the nearest tenth.

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44) In circle E shown below, point D is a point of tangency between circle E and segment CD. What is the value of “x”?

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45) Determine the standard equation for circle M with a radius of 9 and a center point M(4, –5). State the letter of the correct answer.

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46) Determine the standard equation for circle Q with a radius of square root (24) and a center point M(–8, –2). State the letter of the correct answer.

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47) For the given equation, (a) state the coordinates of the center of the circle in the coordinate plane and (b) state the length of the radius.

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48) For the given equation, (a) state the coordinates of the center of the circle in the coordinate plane and (b) state the length of the radius.

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49) Determine the radius for circle Q with center at (–1,–2), and then write the standard equation.

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