In the figure below, $ABCD$ is a square. $E$ and $F$ are on sides $AD$ and $CD$, respectiv

Question

In the figure below, $ABCD$ is a square. $E$ and $F$ are on sides $AD$ and $CD$, respectively, such that $BEF$ is an equilateral triangle. Fold triangle $BEF$ along $BE$ to obtain quadrilateral $EGBF$. Given that angle $DEF = 45^\circ$, find the sizes of angle $BFC$, angle $ABE$, angle $FEG$, angle $ABG$. Hence determine the type(s) of triangles $DEF$ and $EGB$, and the type of quadrilateral $EGBF$, stating your reasons clearly.

Accepted Answer

(a) $\angle BFC=75^\circ$ (b) $\angle ABE=15^\circ$ (c) $\angle FEG=120^\circ$ (d) $\angle ABG=45^\circ$ (e) $\triangle DEF$ is right isosceles, $\triangle EGB$ is equilateral, and $EGBF$ is a rhombus

Triangles and Quadrilaterals

Triangles and Quadrilaterals

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