Question

why is the included angle important in the sas criterion? a. it is the smallest angle b. it is always 90 degrees c. it is the largest angle d. it ensures the two sides are connected correctly if two triangles have ab = de, ac = df, and ∠bac = ∠edf, which congruence rule applies? a. asa b. sss c. aas d. sas in which scenario is sas used? a. verifying two sides and an included angle match b. comparing all angles in two triangles c. checking all three sides of two triangles d. measuring only the perimeter

Explanation:

1. In the SAS (Side - Angle - Side) congruence criterion, the included angle is crucial as it fixes the relative position of the two sides, ensuring the two sides are connected correctly. It has nothing to do with being the smallest, largest, or always 90 - degrees.
2. Given \(AB = DE\), \(AC=DF\), and \(\angle BAC=\angle EDF\), we have two sides and the included - angle equal for the two triangles, so the SAS congruence rule applies.
3. The SAS criterion is used when we are verifying that two sides and the included angle of two triangles match.

Answer:

1. d. It ensures the two sides are connected correctly
2. d. SAS
3. a. Verifying two sides and an included angle match