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I need help to fill it in-example-1

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Answer: See attached. The first is given, then vertical angles, then transitive property of congruence.

Explanation:

The first statement is given. You can see that under the Part A header, it says "Given: ∠CDB ≅ ∠BFE" so we do not need to prove this.

The second statement is "∠CBD ≅ ∠ABF" and looking at the figure shows that these are vertical angles. It is known that vertical angles are congruent, making this the correct reason for this statement.

The third and final statement says "∠ABF ≅ ∠BFE" so we will look at the properties of congruence and the given figure. A reflexive property example is AB = AB, in other words, something is equal to itself. This does not apply here. A symmetric property example is AB = BA, we have one matching segment (BF), but another point in each angle that isn't symmetric with the other. This leads us to the last property of congruence, the transitive property. An example of this is if AB = CD and CD = BC, then AB = BC. We will select this as our reason for the final statement.

I need help to fill it in-example-1
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