Properties of Rectangles


The above diagram shows a rectangle creased at EFEF such that that point CC aligns with point A.A. If BAE=38,\angle BAE=38^\circ, what is EFD\angle EFD in degrees?

Note: The above figure is not drawn to scale.

The figure above depicts a rectangle with AB=5\overline{AB}=5 and AD=13.\overline{AD}=13. Find x+y.x+y.

ABCDABCD is a square. On line segment ABAB, EE is a point such that ADE=37\angle ADE = 37 ^\circ. What is the measure of EDC\angle EDC (in degrees)?

In the diagram above, BCDE\square BCDE is a rectangle with horizontal side length 3030 cm and vertical side length 66 cm. Line segments BD\overline{BD} and CE\overline{CE} are diagonals of BCDE,\square BCDE, which intersect at point OO. Point MM is the bisector of BE,\overline{BE}, and the extension of lines DM\overline{DM} and CB\overline{CB} intersect at point A.A. If point FF is the intersection of CE\overline{CE} and AD,\overline{AD}, what is the area of DOF?\triangle DOF?

Note: The above figure is not drawn to scale.

The diagram above shows a circle centered at O,O, with rectangle ODCE ODCE inscribed in the quarter circle AOB.AOB. If the radius of the circle is 1414, what is the length of line segment DE?\overline{DE}?


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