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Geometry Difficulty 5.7 AIME, harder Prove it

Shnol D.Z.

In quadrilaterals \$ABCD\$ and \$A_1B_1C_1D_1\$, the corresponding angles are equal. In addition, \$AB=A_1B_1\$, \$AC=A_1C_1\$, \$BD=B_1D_1\$. Are the quadrilaterals \$ABCD\$ and \$A_1B_1C_1D_1\$ necessarily equal?

Solution

Let \$A=A_1\$, \$B=B_1\$, \$ on side $ BX\$ \mathrm{~B} X \$ and $D$\$ \mathrm{D} \$, \$ \$AC=AC_1=BD=BD_1\$ and isosceles trapezoids \$ABCD\$, \$A_1B_1C_1D_1\$ satisfy all conditions, but are not equal.

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## Answer

No.

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