Question

EASY GEOMETRY PROOF:

Prove that if two inscribed angles intercept the same arc, then the angles are congruent.

Answer 1

iN THE ABOVE FIGURE
angleBAD and BFD are inscribed in the same arc BFD and intercepts same arc BXB. Hence by inscribed angle theorem we have:
\[\huge \angle BAD = \frac{1}{2} m( arcBXD)---(1)\]

\[\huge \angle BFD= \frac{1}{2} m( arcBXD)---(2)\]
From equations (1) and (2) we have
\[\huge \angle BAD = \angle BFD \rightarrow \angle BAD \cong \angle BFD\]
Thus, the statement
If two inscribed angles intercept the same arc, then the angles are congruent.

Answer 2

@Ferrariwindows7