Chapter Closure
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See solution.
We are given that TC ≅ TM and AT bisects ∠ CTM.
Let's first add this information to the diagram. Note that the definition of bisecting
is to cut something into two equal halves. Therefore, ∠ ATC and ∠ ATM are congruent angles.
Additionally, the triangles △ ATC and △ ATM share AT as a side. By the Reflexive Property of Congruence we know that this side is congruent in our triangles.
Now we have enough information to claim that △ CAT≅ △ MAT by the SAS ≅ condition. Since CA and MA are corresponding parts, we can therefore claim that CA≅ MA. Now we can complete the proof.
Statement
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Reason
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1. TC≅ TM
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1. Given
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2. AT bisects ∠ CTM
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2. Given
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3. ∠ CTA≅ ∠ MTA
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3. Definition of bisect
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4. AT≅ AT
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4. Reflexive Property of Congruence
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5. △ CAT ≅ △ MAT
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5. SAS≅ condition
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6. CA ≅ MA
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6. ≅ Δ s → ≅ parts
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