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Geometry / Mr. Hansen |
Name: _________________________ |
Proof (10 pts.)
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Use a 2-column proof to show that in a kite that is not a rhombus, at least one diagonal is not an angle bisector. |
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Diagram: |
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Given: KITE is a kite with |
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Prove: At least one of |
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1. |
| 1. Given |
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2. KITE is not a rhombus |
| 2. Given |
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3. |
| 3. Assume bwoc [negation of concl.] |
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4. |
| 4. Def. bis. |
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5. |
| 5. PBT |
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6. All 4 angles at A are rt. |
| 6. Def. |
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7. All 4 angles at A are |
| 7. All rt. |
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8. |
| 8. Refl. |
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9. |
| 9. ASA (7, 8, 4) |
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10. |
| 10. CPCTC |
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11. |
| 11. Trans. (1, 10) |
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12. KITE is a rhombus |
| 12. Def. prop. of a
rhombus: 4 sides |
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| Steps 2, 12 |
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(Q.E.D.) |
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Alternate version (streamlined) |
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1. KITE is a kite |
| 1. Given |
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2. KITE is not a rhombus |
| 2. Given |
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3. |
| 3. Assume bwoc [negation of concl.] |
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4. KITE is a rhombus |
| 4. Def. prop. of rhombus: diags. bis. |
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| Steps 2, 4 |
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(Q.E.D.) |
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