Question

given △abc and △dec with congruent parts as marked, what else is needed to show congruence? complete the sentences below. if ab = blank, then there is congruence by blank. alternatively, to use blank, either of the conditions bc = blank or ac = blank is needed. asa aas cpctc

Explanation:

Step1: Recall congruence postulates

We know ASA (Angle - Side - Angle) and AAS (Angle - Angle - Side) are triangle - congruence postulates.

Step2: Analyze given angles

We see that \(\angle BAC\cong\angle EDC\) and \(\angle BCA\cong\angle ECD\) (vertically - opposite angles are equal).

Step3: Determine missing part for ASA

For ASA, if \(AC = DC\), then \(\triangle ABC\cong\triangle DEC\) by ASA.

Step4: Determine missing part for AAS

For AAS, we need either \(BC = EC\) or \(AB = DE\).

Answer:

If \(AC = DC\), then there is congruence by ASA. Alternatively, to use AAS, either of the conditions \(BC = EC\) or \(AB = DE\) is needed.