Question

if statement 7 is $overline{ef} cong overline{gf}$, which reason justifies statement 8?
a) la theorem
b) ll theorem
c) definition of isosceles triangle
d) definition of congruence

1. cpctc
2. $\triangle efg$ is isosceles.
3. $\triangle efh cong \triangle gfh$

Explanation:

To determine the reason for statement 8 (△EFG is isosceles), we analyze the given information. Statement 7 is \( \overline{EF} \cong \overline{GF} \) (from CPCTC, which follows triangle congruence). An isosceles triangle is defined as a triangle with at least two congruent sides. Since \( \overline{EF} \cong \overline{GF} \), by the definition of an isosceles triangle, △EFG must be isosceles. Option C is "Definition of isosceles triangle", which matches this reasoning. Options A (LA Theorem) and B (LL Theorem) relate to right - triangle congruence, not the definition of an isosceles triangle. Option D (Definition of congruence) is about congruent figures in general, not specifically about isosceles triangles.

Answer:

C) Definition of isosceles triangle