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 \(AC = AB\) (marked with the same tick - mark), \(CD=BD\) (marked with the same double - tick mark), and \(AD = AD\) (common side).

Step2: Check congruence criteria

By the Side - Side - Side (SSS) congruence criterion, \(\triangle ADC\cong\triangle ADB\). Also, since \(CD = BD\), the line \(AD\) is the perpendicular bisector (or a line of symmetry) of \(CB\). A reflection across line \(AD\) will map \(\triangle ADC\) onto \(\triangle ADB\)

Answer:

The first drop - down: "a reflection across line \(AD\)" ; The second drop - down: "a rigid transformation"