In SAS congruence, which parts must be congruent?

• A. Not related
• B. Two sides and the included angle
• C. Two angles and the included side
• D. All three sides

Answer: (B)

The key idea is that knowing two side lengths and the angle between them fixes the triangle completely. If two triangles have those same two sides congruent and the included angle congruent, you can align one side with the other and rotate so the angle matches; the third side length is then determined by the two sides and that angle (think of the law of cosines: c^2 = a^2 + b^2 − 2ab cos(C)). Once the third side is fixed, the remaining angles are forced by the triangle sum, so the triangles are congruent. The included angle must be the one between the two known sides; other combinations (like two angles with the included side, or all three sides) are different congruence tests. So the two sides and the included angle is the condition that guarantees SAS congruence.