Question

Melvin began a plan for this proof. since segment ab ≅ segment cd, then ab = cd. he knows that bc = bc, by the reflexive property of equality. what is a possible next step in melvin’s proof?

Answer 1

Melvin's next step in the proof could involve using congruence postulates such as ASA or SAS to establish the congruence of two triangles, provided additional congruent angles or segments are identified.

Step-by-step explanation:

Considering that Melvin has already established that segment AB is congruent to segment CD (AB ≅ CD), and thus AB = CD, and also that BC = BC by the reflexivity property, a possible next step in the proof would involve finding another pair of congruent segments or angles that can lead to establishing the congruence of two triangles or another geometric concept. If the intent is to prove that two triangles are congruent, Melvin could look for the Angle-Side-Angle (ASA) Postulate, Side-Angle-Side (SAS) Postulate, or another congruence rule that matches the given situation. For example, if Melvin knows the corresponding angles between AB and BC in one triangle and CD and BC in another triangle are equal, then he can conclude the triangles are congruent by the ASA Postulate.