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Triangle Congruence and Inequalities 1
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Result
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Identify the missing statements or reasons that will complete the two-column proof. Type the letter of your answer in each blank.

Given: AM ¯ ⊥ AT ¯
MH ¯ ⊥ HT ¯
AT ¯ ≅ TH ¯
Prove: MT → bisects ∠AMH.
Choices:
a. HL Congruence Theorem
b. Vertical Angles Theorem
c. Definition of angle bisector
d. ΔMAT≅ΔMHT
e. ∠MHT
f. ∠AMT≅∠HMT
g. Reflexive Property of Segment Congruence
h. ΔMAT and ΔMHT are right triangles.
i. LL Congruence Theorem
j. Definition of perpendicular segments
k. ∠THM
l. ΔMAT and ΔMTH are right triangles.

Proof:
Statements Reasons
1.
AM ¯ ⊥ AT ¯
MH ¯ ⊥ HT ¯
AT ¯ ≅ TH ¯
1. Given
2.
∠MAT and are right angles.
2.
3.
3. Definition of right triangle
4.
MT ¯ ≅ MT ¯
4.
5.
ΔMAT≅ΔMHT
5.
Statements 1, 3, and 4; and
6.
6. CPCTC
7.
MT → bisects ∠AMH.
7.
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