Question

what is the missing reason in the proof? statements reasons 1. $overline{ab}paralleloverline{cd}$; $overline{bc}paralleloverline{da}$ 1. given 2. quadrilateral abcd is a $parallelogram$ 2. definition of parallelogram 3. $overline{ab}congoverline{cd}$; $overline{bc}congoverline{da}$ 3. opposite sides of a parallelogram are $cong$ 4. $overline{ac}congoverline{ac}$ 4. reflexive property 5. $\triangle abccong\triangle cda$ 5. ? perpendicular bisector theorem

Explanation:

Step1: Recall triangle - congruence postulates

We have $\overline{AB}\cong\overline{CD}$, $\overline{BC}\cong\overline{DA}$, and $\overline{AC}\cong\overline{AC}$. These are three pairs of corresponding sides of $\triangle ABC$ and $\triangle CDA$.

Step2: Identify the postulate

The Side - Side - Side (SSS) congruence postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Answer:

SSS congruence postulate