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For the first two problems, fill in the blanks. |
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Refer to the figure below to answer the next four questions about circle W based on the given information. |
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11) Since angles VSU and SUT are congruent, what is true about chord SV and chord TU? |
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Refer to the figure and the information given below to answer the next two questions. |
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For the remaining figures in this unit, assume that any lines that appear to be tangent to a circle are indeed tangent lines. |
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19) Describe a “point of tangency”. |
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21) In triangle ABC shown below, (a) explain why angle ABC is a right angle, (b) state the length of AC, and (c) determine the value of “x”? |
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24) Common external tangents (do, do not) intersect a line segment that has its endpoints on the centers of the two circles. |
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25) Common internal tangents (do, do not) intersect a line segment that has its endpoints on the centers of the two circles. |
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Activity: Print out the triangle below. Complete the following steps to construct a specific circle. (1) Using a compass, bisect angles A and B, extending the bisectors out so that they intersect. Name the point of intersection, point D. (2) From point D, construct a line perpendicular to segment AB. Name the point of intersection of the bisector and segment AB, point E. (3) Set the metal point of the compass on point D and the pencil point of the compass on point E. This setting is the radius of circle D. (4) Draw circle D. |
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29) Examine the figure and the information given below. Answer the following questions about the figure: (a) Why can it be stated that segments VU and VW are congruent? (b) What property of equality justifies the statement that segment TV is congruent to itself? (c) What theorem in this unit justifies the statement that segments TU and TW are congruent? (d) What postulate can be used to deduce that triangles TUV and TWV are congruent? |
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31) Describe a secant. |
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32) Select the answer that completes Theorem 25-H: If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is _________ the measure of its intercepted arc. |
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33) Select the answer that completes the Theorem 25-I: If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measures of the arcs intercepted by the __________ and its _________ __________. |
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35)
For the figure and the information provided below, answer the following questions: (a) What is the value of “x”? (b) What is the measure of arc AB? (c) What is the measure of arc CD? (d) What is the measure of angle DFC? |
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36) Select the answer that completes the Theorem 25-J: The measure of an angle formed by two secants, a secant and a tangent, or two tangents intersecting in the exterior of a circle is equal to one-half the __________ __________ of the measures of the intercepted arcs. |
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39) For circle L and the information given below, answer the following questions: (a) What is the value of “x”? (b) What is the value of “y”? (c) What is the value of “z”? |
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42) Activity: Modify the steps for constructing a hexagon to make the inscribed six-pointed star below. Explain how you created the star. |
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43) 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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