Question

1. which reason justifies the last step in a proof that △def≅△dab? given: $overline{ad}=overline{ed}$, d is the mid - point of $overline{bf}$. sas postulate cpctc aas theorem asa postulate

Explanation:

The SAS (Side - Angle - Side) Postulate is used to prove two triangles congruent when two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is used after proving two triangles congruent to show that other corresponding parts are congruent. The AAS (Angle - Angle - Side) Theorem is for proving triangles congruent when two angles and a non - included side are congruent. The ASA (Angle - Side - Angle) Postulate is for proving triangles congruent when two angles and the included side are congruent. Since we are looking for the reason to justify the last step in proving $\triangle DEF\cong\triangle DAB$, and assuming we have already established the congruence of the triangles using other means before stating the congruence of corresponding parts, CPCTC is used to conclude congruence of remaining parts after proving the triangles congruent.

Answer:

CPCTC