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}). asa postulate sas postulate cpctc aas theorem

Explanation:

Step1: Recall triangle - congruence postulates and CPCTC

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is used to prove that corresponding parts of two already - proven congruent triangles are equal. The ASA (Angle - Side - Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. The SAS (Side - Angle - Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. The AAS (Angle - Angle - Side) theorem states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent. Here, we are trying to justify the last step of proving $\triangle DEF\cong\triangle DAB$.

Step2: Determine the correct reason

The last step of a proof that two triangles are congruent is usually to state the postulate or theorem that makes them congruent. Since we are proving $\triangle DEF\cong\triangle DAB$, and we assume we have already established the congruence of the necessary parts (sides and angles), the reason for the last step of the proof that $\triangle DEF\cong\triangle DAB$ is one of the triangle - congruence postulates. Given $AD = ED$ and $D$ is the mid - point of $BF$ (which gives $DF=DB$), if we can show that the included angles are equal, we can use the SAS postulate.

Answer:

SAS Postulate