Lines CF,GE are parallel to diagonal DB. Are the cyclic quadrilaterals CBGDC,FBGDF (with same sides and angles) congruent? If not, how are they be described?

Maia Pace

Maia Pace

Answered question

2022-08-11

Lines C F , G E are parallel to diagonal D B.

Are the cyclic quadrilaterals C B G D C , F B G D F (with same sides and angles) congruent? If not, how are they be described?

Answer & Explanation

Angel Burton

Angel Burton

Beginner2022-08-12Added 12 answers

Yes. Draw the line l through the center O perpendicular to D B. Then l passes through the midpoint of D B. Moreover l is orthogonal to C F and G E because the two latter chords are parallel to parallel to D B. Therefore l passes through the midpoints of C F and G E. Consequently a reflection in l maps one quadrilateral into the other.

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