EDGE Math 8

Identify the missing statements or reasons that will complete the two-column proof. Type the letter of your answer in each blank.

Given:	$\bar{A M} ⊥ \bar{A T}$ $\bar{M H} ⊥ \bar{H T}$ $\bar{A T} ≅ \bar{T H}$
Prove:	$\vec{M T}$ bisects $∠ A M H .$

Choices:

a.	HL Congruence Theorem
b.	Vertical Angles Theorem
c.	Definition of angle bisector
d.	$Δ M A T ≅ Δ M H T$
e.	$∠ M H T$
f.	$∠ A M T ≅ ∠ H M T$

g.	Reflexive Property of Segment Congruence
h.	$Δ M A T$ and $Δ M H T$ are right triangles.
i.	LL Congruence Theorem
j.	Definition of perpendicular segments
k.	$∠ T H M$
l.	$Δ M A T$ and $Δ M T H$ are right triangles.

Proof:

Statements

Reasons

\bar{A M} ⊥ \bar{A T}

\bar{M H} ⊥ \bar{H T}

\bar{A T} ≅ \bar{T H}

1. Given

∠ M A T

and are right angles.

3. Definition of right triangle

\bar{M T} ≅ \bar{M T}

Δ M A T ≅ Δ M H T

Statements 1, 3, and 4; and

6. CPCTC

\vec{M T}

bisects

∠ A M H .

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