Question

Determine which postulate or theorem can be used to prove that REM = DME.

Options:
Option 1: SAS
Option 2: ASA
Option 3: AAS
Option 4: SSS

Answer 1

The postulate that can be used to prove that REM = DME is Option 2: ASA (Angle-Side-Angle).

Step-by-step explanation:

In an ASA congruence, if two triangles have two corresponding angles congruent, and the included sides are also congruent, then the triangles are congruent. In this case, we can observe that ∠R ≅ ∠D (Angle), EM ≅ ME (Side), and ∠E ≅ ∠E (Angle). Applying the ASA congruence, we can conclude that triangle REM is congruent to triangle DME.

This congruence can be represented as:

`\[ \triangle REM \cong \triangle DME \]`

Thus, we have established that the given triangles are congruent based on the ASA postulate. The congruence of these triangles implies that the corresponding parts, in this case, REM and DME, are also congruent. Therefore, we can state that REM is equal to DME.

Understanding and applying congruence postulates are fundamental in geometry. The ASA postulate is particularly useful in proving triangles congruent when two angles and the included side are known. This logical approach ensures a solid foundation in geometric reasoning and provides a rigorous basis for mathematical proofs.

So correct option is Option 2: ASA (Angle-Side-Angle).