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 translating reflecting rotating triangle adc maps it onto triangle adb. reset next

Explanation:

Step1: Analyze triangle congruence via transformation

Triangles \(ADC\) and \(ADB\) share side \(AD\). \(AC = AB\) (marked with \(x\)) and \(CD = BD\) (marked with \(||\)). Reflecting \( \triangle ADC \) over line \(AD\) (the axis of symmetry) will map \(C\) to \(B\), \(D\) to \(D\), and \(A\) to \(A\), showing congruence. Translating or rotating wouldn't align them as symmetrically. So the first dropdown is "reflecting", and the second action is "reflecting" (or the transformation that maps \( \triangle ADC \) to \( \triangle ADB \) is reflection over \(AD\)).

Answer:

First dropdown: reflecting; Second action: reflecting (or the transformation is reflection over \(AD\) to map \( \triangle ADC \) to \( \triangle ADB \))