Question

complete the proof that \\( \angle g i h \cong \angle e i f \\).
1 \\( m \angle e i f + m \angle f i g = 180 ^ { \circ } \\)
2 \\( m \angle f i g + m \angle g i h = 180 ^ { \circ } \\) angles forming a linear pair sum to \\( 180 ^ { \circ } \\)
3 \\( m \angle e i f + m \angle f i g = m \angle f i g + m \angle g i h \\) transitive property of equality
4 \\( m \angle e i f = m \angle g i h \\) properties of addition, subtraction, multiplication, and division
5 \\( \angle g i h \cong \angle e i f \\) definition of congruence
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not feeling ready yet? these can help:
identify complementary, supplementary, verti... properties of equality
lesson: complementary angles lesson: supplementary angles
lesson: vertical angles lesson: adjacent angles

Explanation:

Step1: Identify the reason for \(m\angle EIF + m\angle FIG=180^{\circ}\)

Angles \(\angle EIF\) and \(\angle FIG\) form a linear pair. By the definition of a linear pair of angles, the sum of the measures of angles in a linear pair is \(180^{\circ}\).

Answer:

Angles forming a linear pair sum to \(180^{\circ}\)