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Geometry / Mr. Hansen |
Name: _________________________ |
Quiz on Chapter 8 (25 points)
Part I. |
In each case, points J, K, and L form one triangle, and points M, N, and O form another triangle. Sketch both triangles, labeling all points, lengths, and known angle measures. Then state which triangles (if any) are similar, and give a reason. Abbreviations are acceptable. If the triangles are not necessarily similar, try to adjust letter order so that they are similar, but if that is impossible, write "NOT NECESSARILY SIMILAR." |
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1. |
JK = 4.5, KL = 7, mÐK = 40; NO = 9, OM = 14, mÐO = 40 |
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2. |
JK = 4.5, KL = 7, mÐK = 40; NO = 9, OM = 14, mÐM = 40 |
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3. |
JL = 4, JK = 5, KL = 3; OM = 3, ON = 5, MN = 4 |
| Part II. | Solve the following "word problem" by drawing a sketch and applying the appropriate theorem(s). For full credit, show your work and give your answer to the nearest inch. |
| Two 700-foot vertical radio towers are situated 300 feet apart in a large level field. A protractor is affixed to the top of one of the towers and is aligned with the protractor’s base parallel to the ground and its flat face lying in the same plane that contains the towers. At 2:00 p.m., the protractor shows that the sun is 40° above the horizon (i.e., the angle formed by the sun, the tip of the tower, and the horizon is 40° ). At 2:00 p.m., by coincidence, the shadow of the protractor tower exactly touches the base of the other tower. Later in the afternoon, when the protractor reads 20° (because the sun appears to have dipped lower on the horizon), how high above ground is the protractor tower’s shadow on the other tower? |