given: abcd is a parallelogram, $\overline{ac}$ bisects $\angle bcd$ and $\overline{db}$ bisects $\angle abc$. prove: $\overline{ac} \perp \overline{bd}$. step statement reason 1 abcd is a parallelogram $\overline{ac}$ bisects $\angle bcd$ $\overline{db}$ bisects $\angle abc$ given 2 $\angle cbd \cong \angle abd$ an angle bisector divides an angle into two congruent angles 3 $\overline{bc} \parallel \overline{ad}$ opposite sides of a parallelogram are parallel 4 $\angle bca \cong \angle cad$ parallel lines cut by a transversal form congruent alternate interior angles 5 $\angle dca \cong \angle bca$ an angle bisector divides an angle into two congruent angles 6 $\angle cad \cong \angle dca$ transitive property 7 $\overline{ad} \cong \overline{cd}$ in a triangle, sides opposite of congruent angles are congruent try type of statement $\overline{xy} \cong \overline{wz}$ $\angle x \cong \angle y$ $\triangle xyz \cong \triangle tuv$ $\overline{xy} \parallel \overline{wz}$ $\overline{xy} \perp \overline{wz}$ classify a triangle $\angle x$ and $\angle y$ are complementary/supplementary $\angle x$ is a right angle $\overline{xy}$ bisects $\angle x$ $\overline{xy}$ bisects $\overline{wz}$ $xy = \frac{1}{2}wz$ (or $2wz$) $m\angle x = \frac{1}{2}m\angle y$ (or $2m\angle y$) note: $bd$ and $\overline{ac}$ are segments. you m e in order to submit.

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# Explanation:
## Step1: Identify ABCD as rhombus
Since $AD \cong CD$ (Step7) and $ABCD$ is a parallelogram, a parallelogram with adjacent congruent sides is a rhombus.
## Step2: Use rhombus diagonal property
In a rhombus, the diagonals are perpendicular to each other.
# Answer:
$\overline{AC} \perp \overline{BD}$

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To complete the proof table, the missing steps (after Step7) would be:
## Step8:
**Statement**: $ABCD$ is a rhombus
**Reason**: A parallelogram with a pair of adjacent congruent sides is a rhombus
## Step9:
**Statement**: $\overline{AC} \perp \overline{BD}$
**Reason**: The diagonals of a rhombus are perpendicular

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Question

Explanation:

Step1: Identify ABCD as rhombus

Step2: Use rhombus diagonal property

Answer:

Step8:

Step9: