Question

select the correct answer from each drop-down menu. why are triangles adc and adb congruent? triangle adc is congruent to triangle adb because reflecting triangle adc options: 90 degrees clockwise, across line segment ac, across line segment ad, to the right maps it onto triangle adb. (diagram: triangle abc with d on bc, ad as a segment, ac and ab marked equal, cd and db marked equal.)

Explanation:

To determine why \(\triangle ADC\) and \(\triangle ADB\) are congruent, we analyze the diagram: \(AD\) is a common side, \(AC = AB\) (marked equal), and \(CD = BD\) (marked equal). Reflecting \(\triangle ADC\) across \(AD\) maps \(C\) to \(B\) (since \(CD = BD\) and \(AC = AB\)), so this reflection maps \(\triangle ADC\) to \(\triangle ADB\), proving congruence.

Answer:

reflecting; across line segment AD