To fill in the blank for Reason 2, we need to identify a geometric property or theorem that justifies the statement "triangle A is congruent to triangle E." Since M triangle A and M triangle E are related in the context provided, a suitable reason would typically involve congruence postulates or theorems.
A common reason for triangle congruence is:
"Corresponding angles are congruent"
This suggests that angles in triangle A correspond to angles in triangle E, confirming their congruence based on angle relationships.
Thus, the completed justification would read:
- M triangle A + 180 Reason 1: Linear pairs are supplementary
- Triangle A is congruent to triangle E: Reason 2: Corresponding angles are congruent
- M triangle E + M triangle C = 180: Reason 3: Substitution
- Triangle E and C are supplementary: Reason 4: Definition of supplementary angles
If there are specific properties or angles involved in triangles A and E that might lead to a different reasoning, that context could lead to other potential justifications.
8 answers