Question

what additional information is needed to prove the triangles are congruent by the sas postulate

Answer 1

You need to know that AC ⊥ BD to use the SAS postulate.

(This makes ∠ACB = ∠ACD. These angles are the angles between the pairs of congruent sides, making SAS applicable.)

Answer 2

Answer:

$AC\perp BD$

Step-by-step explanation:

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.    

We can see from our given graph that triangle ABD is divided in two smaller triangles ACB and ACD.  

We have been given that side BC equals to side DC. We can see that in triangles ACB and ACD side AC equals to itself.  

In order to triangles ACB and ACD be congruent by SAS postulate measure of angle ACB  and ACD must be equal.      

We can see that angle ACB  and angle ACD form an linear pair, So $m\angle ACB+m\angle ACD=180^{o}$

If we are given that AC is perpendicular to BD then measure of ACB will be equal to ACD as a perpendicular meets a line at a right angle.

$90^{o}+m\angle ACD=180^{o}$

$m\angle ACD=180^{o}-90^{o}$  

$m\angle ACD=90^{o}$  

$m\angle ACB=m\angle ACD=90^{o}$    

Therefore, the additional information that will prove the triangles ACB and ACD congruent by SAS postulate is $AC\perp BD$.