Question

question given: $overline{ab}perpoverline{bc},overline{ad}perpoverline{dc}$ and $overline{bc}paralleloverline{ad}$. prove: $\triangle abccong\triangle cda$. step 1 $overline{ab}perpoverline{bc}$ $overline{ad}perpoverline{dc}$ $overline{bc}paralleloverline{ad}$ try type of statement

Explanation:

Step1: Identify right - angles

Since $\overline{AB}\perp\overline{BC}$ and $\overline{AD}\perp\overline{DC}$, $\angle B = \angle D=90^{\circ}$.

Step2: Use parallel - line property

Because $\overline{BC}\parallel\overline{AD}$, $\angle BCA=\angle DAC$ (alternate interior angles).

Step3: Identify common side

$\overline{AC}=\overline{AC}$ (reflexive property).

Step4: Apply AAS congruence

In $\triangle ABC$ and $\triangle CDA$, we have $\angle B=\angle D$, $\angle BCA = \angle DAC$, and $\overline{AC}=\overline{AC}$. By the Angle - Angle - Side (AAS) congruence criterion, $\triangle ABC\cong\triangle CDA$.

Answer:

The proof is completed as above, showing that $\triangle ABC\cong\triangle CDA$ by AAS.