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 triangle adc maps it onto triangle adb

Explanation:

Step1: Analyze the triangles

We observe that \(AD\) is a common side for both \(\triangle ADC\) and \(\triangle ADB\). Also, \(AC = AB\) (marked with the same tick - marks) and \(CD=BD\) (marked with the same tick - marks). The line \(AD\) acts as the axis of symmetry.

Step2: Determine the transformation

When we reflect \(\triangle ADC\) over the line \(AD\), the point \(C\) maps to point \(B\) (since \(CD = BD\) and \(AD\) is common). The side \(AC\) maps to side \(AB\) (since \(AC = AB\)).

Answer:

The first drop - down: reflecting; the second drop - down: over the line \(AD\)