Question
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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?
To prove the triangles congruent by SAS (Side-Angle-Side), we need to know the following information:
1. The length of side AC: In order to apply the side-angle-side (SAS) congruence criterion, we must know that the two triangles share a common side AC.
2. The measures of angles DAC and ACB: Additionally, we need to know the measures of these two angles, as SAS requires that the corresponding sides be in the same order with the included angles.
To prove the triangles congruent by SAS (Side-Angle-Side) postulate, you would need to know the following additional information:
1. The length of one side of both triangles: Knowing the length of one side in each triangle helps establish the side part of the SAS postulate.
2. The measure of the included angle: The included angle is the angle between the two known sides. It helps establish the angle part of the SAS postulate.
Once you have the lengths of one side in each triangle and the measure of the included angle, you can compare the corresponding sides and angles in the triangles to show that they are congruent.
To prove the triangles congruent by SAS (Side-Angle-Side), we need to know the following:
1. We need to know that both triangles have two pairs of congruent sides. This means that we need to know the lengths of two sides in both triangles.
2. We also need to know that one pair of corresponding sides is congruent in both triangles. This means that we need to know the length of the side shared by both triangles.
In the given diagram, we have a quadrilateral ABCD with a diagonal segment from A to C. We are given that angle DAC and angle ACB are marked with an arc.
To prove the triangles congruent by SAS, we will need one additional piece of information. We need to know either the length of one of the remaining sides or the measure of another angle in either triangle.
If we are given the length of one side in both triangles or the measure of one angle in either triangle, we can compare the corresponding sides and angles to show that the triangles are congruent using the SAS congruence postulate. Without this additional information, we cannot prove the triangles congruent by SAS.