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Problem 468: Circle, Chord, Midpoint, Congruence, Angle.
Level: High School, College, SAT Prep.

The figure shows a circle O and equal chords AB, CD, EF, and GH. If M, N, P, and Q are the midpoints of AB, CD, EF, and GH, respectively, prove that angles MPN and MQN are congruent.

Circle, Chord, Congruence, Angle
 
 


 

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."
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