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In the figure above, DF is the diameter of the semicircle. Rectangle ABCD and BEFG are congruent, and EF is on the diameter DF. Find the measure of ∠ABG.

 #1
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The only thing you are "absolutely destroying" is your own education as you 'outsource' your homework questions .

 Apr 6, 2024
edited by Holtran  Apr 6, 2024
 #2
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Note that since the rectangles are congruent, we have DB = BF. That would imply \(\angle BDF = \angle BFD\). Also, BE is perpendicular to EF, so \(\angle BED = \angle BEF = 90^\circ\). Together with the common side BE we have the pair of congruent triangles \(\triangle DEB \cong \triangle FEB\). Consequently we have the fact that E is the centre of the semi-circle. So we now have enough information to figure out that \(\triangle DAE\) is equilateral. The rest is done through some angle chasing, which is not hard.

 Apr 8, 2024

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