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Given a circle (1), the lines AED (2)
and BFC (3). If AB is parallel to CD, prove that the angles AFB
and AEB are equal.
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HINTS:
PARALLEL LINES
Proposition. If two lines are parallel,
each pair of alternate interior angles are congruent. Also
converse.
ANGLES IN A CIRCLE
Proposition. An inscribed angle is measured by
one-half its intercepted arc.
CYCLIC QUADRILATERAL is a
quadrilateral whose vertices all lie on a single circle.
Proposition 1.
Opposite angles of a cyclic
(inscribed) quadrilateral are supplementary. Also converse.
Proposition 2. A quadrilateral is cyclic if one side subtends
congruent angles at the two opposite vertices. Also
converse.
See also:
Problem 71
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