Question

question 8 (multiple - choice worth 1 points) (02.04 mc) the figure below shows rectangle abcd with diagonals $overline{ac}$ and $overline{db}$. jimmy wrote the following proof to show that the diagonals of rectangle abcd are congruent: jimmys proof: statement 1: rectangle abcd is given. statement 2: $overline{ab}congoverline{dc}$ because opposite sides of a rectangle are congruent. statement 3: angles abc and dcb are both right angles by definition of a rectangle. statement 4: angles abc and dcb are congruent because all right angles are congruent. statement 5: triangles abc and dcb are congruent by sas. statement 6: $overline{ac}congoverline{db}$ by cpctc. which statement below completes jimmys proof? $overline{ad}congoverline{ad}$ (reflexive property of congruence) $overline{ad}congoverline{ad}$ (transitive property of congruence) $overline{bc}congoverline{bc}$ (reflexive property of congruence) $overline{ac}congoverline{bc}$ (transitive property of congruence)

Explanation:

To prove $\triangle ABC\cong\triangle DCB$ by SAS (Side - Angle - Side) congruence criterion, we already have $AB\cong DC$ (opposite sides of rectangle) and $\angle ABC\cong\angle DCB$ (right - angles of rectangle). We need the included side between these angles. The included side for $\angle ABC$ and $\angle DCB$ in the two triangles is $BC$. By the reflexive property of congruence, $\overline{BC}\cong\overline{BC}$.

Answer:

$\overline{BC}\cong\overline{BC}$ (reflexive property of congruence)