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Geometry / Mr. Hansen |
Name: _______________________ |
Two Proofs from §15.3 (Hinge Theorem)
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p.700, #14. |
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1. AC < AE |
1. Given |
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2. D mdpt. of sCE |
2. Given |
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3. CB = FE |
3. Given |
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4. AE > AC [optional step] |
4. Restatement of 1 |
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5. ÐC > ÐE |
5. Larger Ð opp. longer side [§15.2] |
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6. CD = DE |
6. Def. mdpt. |
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7. BD > FD |
7. Hinge Thm. (steps 3, 6, 5) |
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Q.E.D. |
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p.700, #16. |
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1. ÐC > ÐA |
1. Given |
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2. AE > CE |
2. Larger Ð opp. longer side |
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3. ÐD > ÐB |
3. Given |
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4. EB > ED |
4. Larger Ð opp. longer side |
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5. AE + EB > CE + ED |
5. Add. prop. [add inequalities in steps (2) and (4): “larger + larger” must exceed “smaller + smaller”] |
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6. AB > CD |
6. Subst. (def. of segment addition) |
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Q.E.D. |
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