Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
Chapter Closure

Exercise 121 Page 423

To bisect something means to cut into two congruent halves.

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
Reason
1.
TC≅ TM
1.
Given
2.
AT bisects ∠ CTM
2.
Given
3.
∠ CTA≅ ∠ MTA
3.
Definition of bisect
4.
AT≅ AT
4.
Reflexive Property of Congruence
5.
△ CAT ≅ △ MAT
5.
SAS≅ condition
6.
CA ≅ MA
6.
≅ Δ s → ≅ parts