Question

given: (overline{ac}congoverline{ad},overline{cb}congoverline{db}) prove: (\triangle abccong\triangle abd)

Explanation:

Step1: Identify the common side

In triangles \( \triangle ABC\) and \( \triangle ABD\), side \(AB\) is common. So, \(AB = AB\) (Reflexive property of equality).

Step2: List the given equal sides

We are given \(AC\cong AD\) and \(CB\cong DB\).

Step3: Apply SSS (Side - Side - Side) congruence criterion

Since \(AC = AD\), \(CB=DB\), and \(AB = AB\), by the SSS (Side - Side - Side) congruence criterion, \( \triangle ABC\cong\triangle ABD\).

Answer:

1. \(AB = AB\) (Reflexive property)
2. \(AC = AD\) (Given)
3. \(CB = DB\) (Given)
4. \( \triangle ABC\cong\triangle ABD\) (SSS congruence criterion)