2. Section 7.2
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Use the given information to prove that two angles and the included side of the triangles are congruent.
See solution.
Let's add the given information that BC∥ EF, AB∥ DE, and AF=DC.
In △ ABC and △ DEF we see that their horizontal sides share FC. Therefore, FC=FC according to the Reflexive Property of Congruence.
Now we have enough information to claim that AC=DF. If we separate the triangles, we see that two pairs of angles and the included side are congruent.
With this information we can claim congruence by the ASA Congruence Theorem. As seen in the diagram, BC and EF are corresponding sides, which means they are congruent. Now we can complete the table.
Statements
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Reasons
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1. BC∥ EF
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1. Given
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2. m∠ BCF = m∠ EFC
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2. Alternate Interior Angles Theorem
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3. AB∥ DE
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3. Given
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4. m∠ BAC = m∠ EDF
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4. Alternate Interior Angles Theorem
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5. AF=DC
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5. Given
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6. FC=FC
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6. Reflexive Property of Equality
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7. AF+FC=FC+DC
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7. Additive Property of Equality
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8. AC=DF
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8. Segment addition
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9. △ ABC ≅ △ DEF
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9. ASA Congruence Theorem
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10. BC ≅ EF
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10. ≅ Δ s → ≅ parts
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