Question

(a) problem 11: (first taught in lesson 38)
from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement.
given: △deg≅△fge
prove: ∠dge≅∠feg

Explanation:

Step1: Recall congruent - triangle property

When two triangles $\triangle DEG$ and $\triangle FGE$ are given as congruent ($\triangle DEG\cong\triangle FGE$), all corresponding parts (sides and angles) of these congruent triangles are equal.

Step2: Identify corresponding angles

$\angle DGE$ in $\triangle DEG$ and $\angle FEG$ in $\triangle FGE$ are corresponding angles. Since the triangles are congruent, by the property that corresponding parts of congruent triangles are congruent (CPCTC), we can conclude that $\angle DGE\cong\angle FEG$.

Answer:

Corresponding parts of congruent triangles are congruent (CPCTC)