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In the figure below, ray was constructed starting from rays and . By using a compass D and G were marked equidistant from E on rays and . The compass was then used to locate a point F, distinct from E, so that F is equidistant from D and G. For all constructions defined by the above steps, the measures of ∠DEF and ∠GEF:

In the figure below ray was constructed starting from rays and By using a compass D and G were marked equidistant from E on rays and The compass was then used class=

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Answer:

The measures of ∠DEF and ∠GEF are the same

Step-by-step explanation:

Connect points D and F and points G and F. Consider triangles EDF and EGF. In these tirangles,

  • ED is congruent to EG because points D and G were marked equidistant from E;
  • DF is congruent to GF because point F, distinct from E, is equidistant from D and G;
  • EF is congruent to EF by reflexive property.

Thus, triangles EDF and EGF are congruent by SSS postulate.

Congruent triangles have congruent corresponding parts, then

[tex]\angle FED\cong \angle FEG[/tex]

Congruent angles have the same measures

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