Question

given: \\(\overline{ab} \cong \overline{ad}; \overline{bc} \cong \overline{dc}\\) prove: \\(\angle abc \cong \angle adc\\) statements reasons 1. \\(\overline{ab} \cong \overline{ad}; \overline{bc} \cong \overline{dc}\\) 1. given 2. \\(\overline{ac} \cong \overline{ac}\\) 2. reflexive property of congruence 3. \\(\triangle abc \cong \triangle adc\\) 3. 4. \\(\angle abc \cong \angle adc\\) 4. which reason justifies step 4?

Explanation:

Step1: Analyze Triangle Congruence

We have \(\triangle ABC\) and \(\triangle ADC\) with \(AB\cong AD\), \(BC\cong DC\), and \(AC\cong AC\) (reflexive property). So, \(\triangle ABC\cong\triangle ADC\) by SSS (Side - Side - Side) congruence criterion.

Step2: Determine the Reason for Step 4

In step 3, we established that \(\triangle ABC\cong\triangle ADC\). By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, the corresponding angles \(\angle ABC\) and \(\angle ADC\) are congruent. So the reason for step 4 (\(\angle ABC\cong\angle ADC\)) is CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

Answer:

The reason that justifies Step 4 is "Corresponding Parts of Congruent Triangles are Congruent (CPCTC)".