Chapter Test
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What can we say about ∠ ACB and ∠ ECD?
See solution.
We also have to show that the included angles, ∠ ACB and ∠ DCE are congruent as well.
If we look at the diagram, we see that ∠ ACB and ∠ ECD are vertical angles. According to the Vertical Angles Congruence Theorem, vertical angles are congruent.
Since we now know that two sides and the included angle of △ ABC are congruent to two sides and the included angle of △ EDC, we can claim by the SAS Congruence Theorem that the triangles are congruent.
Let's also show this as a two-column proof.
Statement
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Reason
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1. CA ≅ CB≅ CD ≅ CE
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1. Given
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2. ∠ ACB ≅ ∠ ECD
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2. Vertical Angles Congruence Theorem
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3. △ ABC ≅ △ EDC
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3. SAS Congruence Theorem
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