Question

1 abcd is a parallelogram 1 given 2 ∠amb, ∠bmc, ∠cmd and ∠dma are right angles 2 given 3 ∠amb ≅ ∠bmc ≅ ∠cmd ≅ ∠dma 3 right angles are congruent 4 ac bisects bd bd bisects ac 4 diagonals of a parallelogram bisect each other 5 am ≅ mc, mb ≅ md 5 definition of a bisector 6 6 sas congruency theorem 7 ab ≅ bc, cb ≅ ba 7 cpctc 8 figure abcd is a rhombus 8 definition of a rhombus which is the missing statement in step 6? △abc ≅ △adc ≅ △bad ≅ △bcd △amb ≅ △cmd ≅ △bad ≅ △bcd △amb ≅ △cmb ≅ △cmd ≅ △amd

Explanation:

Step1: Analyze the SAS congruency theorem

The SAS (Side - Angle - Side) congruency theorem requires two sides and the included angle to be congruent. In the context of the parallelogram's diagonals, we have \(AM = MC\), \(MB=MD\), and \(\angle AMB=\angle BMC = \angle CMD=\angle DMA\) (right angles).

Step2: Identify the triangles for congruency

We need to find four triangles that have two sides (from the bisected diagonals) and the included right - angle congruent. The triangles \(\triangle AMB\), \(\triangle BMC\), \(\triangle CMD\), and \(\triangle AMD\) fit this criterion.

Answer:

\(\triangle AMB\cong\triangle BMC\cong\triangle CMD\cong\triangle AMD\)