Question

given that $overline{ad}=overline{cb}$, and $overline{dc}=overline{ba}$, prove that $\triangle adc=\triangle cba$.
statement\treason

1. $overline{ad}=overline{cb}$\tgiven
2. $\triangle adc=\triangle cba$\tsss
3. $overline{dc}=overline{ba}$\tgiven
4. $overline{ac}=overline{ac}$\treflexive property of congruence

the proof shown is written in an incorrect order. what is a possible order that the statements and reasons could be written in?
2, 3, 1, 4
two of these
2, 4, 3
1, 3, 4, 2

Explanation:

Step1: List given sides first

We start with the given side - equalities. So, we first state $\overline{AD}=\overline{CB}$ (Statement 1) and $\overline{DC}=\overline{BA}$ (Statement 3) as they are given facts.

Step2: Use reflexive property

Then, we use the reflexive property of congruence to state $\overline{AC}=\overline{AC}$ (Statement 4) since it is a side common to both $\triangle ADC$ and $\triangle CBA$.

Step3: Apply SSS criterion

Finally, with all three pairs of corresponding sides equal, we can prove $\triangle ADC\cong\triangle CBA$ using the SSS (Side - Side - Side) congruence criterion (Statement 2).

Answer:

D. 1, 3, 4, 2