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1 Section 4.3.2: 10) Here are some introductory exercises about congruence theorems. a) What does it mean for two triangles to be congruent ? b) You may assume that SSS , SAS , and ASA are all valid congruence theorems. Discuss and draw a picture illustrating the meaning of each of these theorems. c) Is A AS a valid triangle congruence theorem? If so, brieﬂy show how it follows from the congruence theorems in part (b). If not, produce a counterexample. d) Repeat part (c) for AAA and SSA . 11) Here we connect the Law of Cosines with SSS . a. Does the value of cos γ uniquely determine an angle γ satisfying 0 ≤ γ ≤ π ? Why? b. Use the Law of Cosines to show that if we know all three sides of a triangle (say, of lengths A, B, and C), then we can uniquely determine all three angles. How does part (a) play a role in this process? c. Construct a large triangle. Measure the three side lengths. Then, use the Law of Cosines to compute the cosine of each of the angles in the
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