Lesson 7.4 - Arcs and Angles
Mr.D's Geometry Class
Investigation 1 |
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1) There are the two TYPES of angles involved here. What are they? 2) Move point D around. From what you observe, what do the observe about the relationship in angle measure between the two types of angles involved? 3) COMPLETE AND PUT IN YOUR CONJECTURE LIST: The measure of an inscribed angle is ______________________. |
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Investigation 2 |
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4) Look at the intercepted arc DB for angle DCB. 5) Move point D around. From what you observe, what do the observe about the relationship between the angle measure and the arc measure? 6) COMPLETE AND PUT IN YOUR CONJECTURE LIST:
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Investigation 3 |
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7) Look at the intercepted arc DB for angle DCB. 8) Move point D around so that the measure of the arc is 180 degrees. What is the measure of angle DCB? 9) What kind of triangle is involved here? 10) Since the angle is 180, what kind of angle is it? 11) Essentially, what has that angle become in relation to the circle? 12) What does that angle cut the circle into? 13) Make a conjecture about this: COMPLETE AND PUT IN YOUR CONJECTURE LIST: Angles inscribed in a semicircle ________________. |
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Investigation 4 |
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14) Notice that there are two inscribed angles here that intercept the same arc. 15) Move points D and B. What do you notice about their angle measures? 16) Make a conjecture about this: COMPLETE AND PUT IN YOUR CONJECTURE LIST: Inscribed angles that incercept the same ___________________. |
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Investigation 5 |
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17) Manipulate the parallel lines in the investigation. 18) What do you observe about the arc measures between the parallel lines? 19) Make a conjecture about this: COMPLETE AND PUT IN YOUR CONJECTURE LIST: Parallel lines incercept ___________ arcs on a circle. |
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Investigation 6 |
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20) A quadrilateral inscribed in a circle is called a CYCLIC QUADRILATERAL. 21) Manipulate the vertices of the quadrilateral. 22) What do you observe about the relationship between the opposite angles in the quadrilateral? 23) Make a conjecture about this: COMPLETE AND PUT IN YOUR CONJECTURE LIST: The _____________ angles of a quadrilateral inscribed in a circle are __________. |
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