Question

1. complete the flowchart proof. then write a two - column proof. give $overline{ab}perpoverline{bc},overline{dc}perpoverline{bc}$. prove $angle b=angle c$. statements reasons

Explanation:

Step1: Recall perpendicular - line definition

Since $\overline{AB}\perp\overline{BC}$, $\angle B = 90^{\circ}$ by the definition of perpendicular lines (two lines are perpendicular if they intersect to form a right - angle).

Step2: Recall perpendicular - line definition again

Since $\overline{DC}\perp\overline{BC}$, $\angle C=90^{\circ}$ by the definition of perpendicular lines.

Step3: Use angle - congruence property

If $\angle B = 90^{\circ}$ and $\angle C = 90^{\circ}$, then $\angle B\cong\angle C$ because all right angles are congruent.

Answer:

Statements	Reasons
$\angle B = 90^{\circ}$, $\angle C = 90^{\circ}$	Definition of perpendicular lines
$\angle B\cong\angle C$	All right angles are congruent