complete the proof that $\angle eif \cong \angle gih$.
diagram: vertical line with points e (top), i (middle), g (bottom); another line through i with points h (left) and f (right), forming angles.
| | statement | reason |
|---|------------------------------------|-----------------------------------------------------------------------|
| 1 | $m\angle eif + m\angle fig = 180^\circ$ | angles forming a linear pair sum to $180^\circ$ |
| 2 | $m\angle fig + m\angle gih = 180^\circ$ | angles forming a linear pair sum to $180^\circ$ |
| 3 | $m\angle eif + m\angle fig = m\angle fig + m\angle gih$ | transitive property of equality |
| 4 | $m\angle eif = m\angle gih$ | properties of addition, subtraction, multiplication, and division |
| 5 | $\angle eif \cong \angle gih$ | blank reason box |

Question

complete the proof that $\angle eif \cong \angle gih$.
diagram: vertical line with points e (top), i (middle), g (bottom); another line through i with points h (left) and f (right), forming angles.
|   | statement                          | reason                                                                 |
|---|------------------------------------|-----------------------------------------------------------------------|
| 1 | $m\angle eif + m\angle fig = 180^\circ$ | angles forming a linear pair sum to $180^\circ$                       |
| 2 | $m\angle fig + m\angle gih = 180^\circ$ | angles forming a linear pair sum to $180^\circ$                       |
| 3 | $m\angle eif + m\angle fig = m\angle fig + m\angle gih$ | transitive property of equality                                       |
| 4 | $m\angle eif = m\angle gih$           | properties of addition, subtraction, multiplication, and division      |
| 5 | $\angle eif \cong \angle gih$         | blank reason box                                                     |

Accepted Answer

# Explanation:
## Step1: Recall the definition of congruent angles
If two angles have equal measures, then they are congruent. This is the definition of congruent angles.
## Step2: Apply the definition to the given angles
We know from step 4 that $ m\angle EIF = m\angle GIH $. By the definition of congruent angles (if $ m\angle A = m\angle B $, then $ \angle A \cong \angle B $), we can conclude that $ \angle EIF \cong \angle GIH $.

# Answer:
If two angles have equal measures, then the angles are congruent (Definition of Congruent Angles)

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the definition of congruent angles

Step2: Apply the definition to the given angles

Answer:

	statement	reason
2	$m\angle fig + m\angle gih = 180^\circ$	angles forming a linear pair sum to $180^\circ$
3	$m\angle eif + m\angle fig = m\angle fig + m\angle gih$	transitive property of equality
4	$m\angle eif = m\angle gih$	properties of addition, subtraction, multiplication, and division
5	$\angle eif \cong \angle gih$	blank reason box