Question

given: \\(\overline{ac} \perp \overline{bd}\\) and \\(\overline{bd}\\) bisects \\(\overline{ac}\\).
prove: \\(\triangle abd \cong \triangle cbd\\).
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$$\begin{tabular}{|c|c|c|} \\hline step & statement & reason \\\\ \\hline 1 & \\(\\overline{ac} \\perp \\overline{bd}\\) \\\\ \\(\\overline{bd}\\) bisects \\(\\overline{ac}\\). & given \\\\ \\hline 2 & \\(\\overline{ad} \\cong \\overline{cd}\\) & a segment bisector divides a segment into two congruent segments \\\\ \\hline 3 & \\(\\overline{bd} \\cong \\overline{bd}\\) & reflexive property \\\\ \\hline 4 & \\(\\angle bda\\) is a right angle & perpendicular lines form right angles \\\\ \\hline \\multicolumn{3}{|l|}{type of statement} \\\\ \\hline \\end{tabular}$$

Explanation:

Answer:

$\angle BDC$ is a right angle, Perpendicular lines form right angles, $\angle BDA\cong\angle BDC$, All right angles are congruent, $\triangle ABD\cong\triangle CBD$, SAS