Answer:
Check below please.
Step-by-step explanation:
Hi,
Let's plot the figure, 1 square and 2 equilateral triangles.
1) Let's remember all the angles we already know, from the square and the equilateral triangle from their respective definition.
In other words:
Statement Reason
[tex]\angle A=\angle B=\angle C=\angle D=90^{\circ}[/tex] Given
[tex]\bigtriangleup AED \cong \bigtriangleup BFC[/tex] [tex]\overline{AE}\cong \overline{AD}\cong \overline{ED} \:and\: A\widehat{E}D\cong A\widehat{D}E\cong D\widehat{A}E=60^{\circ}\\\overline{BF}\cong \overline{FC}\cong \overline{BC} \:and\: A\widehat{E}D\cong A\widehat{D}E\cong D\widehat{A}E=60^{\circ}\\[/tex]
2) We have two triangles ABF and CDE
[tex]\bigtriangleup ABF, \:and \bigtriangleup CDE \\A\widehat{B}F=C\widehat{D}E=90^{\circ}+60^{\circ}=150^{\circ}[/tex]
3) The Side, Angle Side Congruence Theorem assures us that both triangles are congruent. When there are two known legs (4 cm and 4 cm) of each triangle, and their respective formed angle is also known (150º). Therefore, these two triangles are both congruent.
Statement Reason
[tex]\overline{DE}\cong \overline{DC} \cong\:\overline{AB}\cong \:\overline{BF} \:and \:C\widehat{D}E \cong A\widehat{B}F[/tex] [tex]SAS \:Theorem[/tex]
