Question

step statement reason
1 ( bd = bc + cd ) multiplication and division properties
2 ( eg = ef + fg ) substitution property
3 ( bd = eg ) given
4 ( bc + cd = ef + fg ) segment addition property
5 ( bc = fg ) given
6 ( fg + cd = ef + fg ) addition and subtraction properties
7 ( cd = ef ) reflexive property

Explanation:

Step1: Segment Addition Property

Segments can be added. So, \(BD = BC + CD\) and \(EG=EF + FG\) are based on the Segment Addition Property.

Step2: Substitution

Since \(BD = EG\) (given), substitute \(BD\) with \(BC + CD\) and \(EG\) with \(EF + FG\) in the equation \(BD = EG\). We get \(BC + CD=EF + FG\).

Step3: Substitute \(BC\) with \(FG\)

Given \(BC = FG\), substitute \(BC\) in \(BC + CD=EF + FG\). So, \(FG + CD=EF + FG\).

Step4: Subtraction Property of Equality

Subtract \(FG\) from both sides of the equation \(FG + CD=EF + FG\). Using the subtraction property of equality (\(a + b=c + b\Rightarrow a=c\)), we get \(CD = EF\).

Answer:

The correct reasons for each step should be:

1. Segment Addition Property
2. Segment Addition Property
3. Given
4. Substitution Property
5. Given
6. Substitution Property
7. Subtraction Property of Equality