Question

1. which congruence postulate or theorem can be used to prove △adc≅△bcd if ad¯≅bc¯? sss congruence postulate sas congruence postulate ssa congruence postulate hl theorem

Explanation:

Step1: Identify given information

We know that \(AD\cong BC\), \(DC = DC\) (common - side), and \(\angle ADC=\angle BCD = 90^{\circ}\) (rectangle properties).

Step2: Recall congruence postulates

The Side - Angle - Side (SAS) congruence postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle ADC\) and \(\triangle BCD\), \(AD\cong BC\), \(\angle ADC=\angle BCD\), and \(DC\) is common.

Answer:

SAS Congruence Postulate