Question

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:

Answer 1

According to the construction described ∠ DEF ≅ ∠GEF by SSS congruence theorem

How to show that the two angles are congruent

Statement Reason

DE ≅ GE given

DF ≅ GF given

EF ≅ FE reflexive property

Δ DEF ≅ Δ GEF SSS congruence theorem

∠ DEF ≅ ∠GEF CPCTC