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Quadrilateral A B C D is shown with a diagonal segment from A to C. Angle D A C is marked with 1 arc. Angle A C B is marked with 1 arc.

What else must you know to prove the triangles congruent by SAS?

AB and CD are parallel

That makes the two angles alternate interior angles. See what you can do with that.

Well, to prove the triangles congruent by SAS, we need to know the length of the segments, not just the angles. So, besides the angles, we also must have information about the side lengths of the triangles. Without that information, we won't be able to prove the congruence. It's like trying to bake a cake without all the ingredients - you're just left with a mess! So, to summarize, we need to know the lengths of both the diagonal segment AC and the side AB in order to prove the triangles congruent by SAS. It's all about having the right ingredients, my friend!

To prove the triangles congruent by SAS (Side-Angle-Side), we need to know the following:

1. Lengths of the sides: We need to know if the lengths of the corresponding sides of the two triangles are equal. In this case, we should know the lengths of the sides AB and CD.

2. Measurement of the included angle: We need to know the measurement of the angle between the two sides. In this case, we know the measurement of angle DAC and angle ACB.

So, to prove the triangles congruent by SAS, we need to know the lengths of the sides AB and CD, and the measures of angles DAC and ACB.

To prove the triangles congruent by SAS (Side-Angle-Side), we need to establish that the corresponding sides and included angle of the triangles are congruent.

In the given diagram, we are provided with the diagonal segment from point A to C, and the angles DAC and ACB are marked with arcs. However, to apply the SAS congruence criterion, we need to know the length of at least one side of each triangle.

Therefore, in addition to the information given, we must also know the length of either side AB or side CD to prove the triangles congruent by SAS. Without knowing the length of either side, we cannot establish the congruence of the triangles based on the SAS criterion.