Geometry Quiz on Congruent Figures

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Refer to the diagram and decide which of the following must be true?

•  $\Delta XSF\ \cong\ \Delta XTG$  

•  $\Delta SXF\ \cong\ \Delta GXT$  

•  $\Delta FXS\ \cong\ \Delta XGT$  

•  $\Delta FXS\ \cong\ \Delta GXT$  

The triangles in the diagram are congruent. Which of the following statements must be true?

• $\angle A\ \cong\ \angle D$

• $\angle B\ \cong\ \angle E$

• $\overline{AB}\ \cong\ \overline{DE}$

• $\overline{BC}\ \cong\ \overline{FD}$

Trapezoid ABCD  $\cong$  trapezoid FGHJ. What is  $m\angle J$  ?

•  $135\degree$  

•  $45\degree$  

•  $90\degree$  

•  $145\degree$  

 $\Delta RST\ \cong\ \Delta XYZ$ . 

Which of the following can't be true?

•  $\angle R\ \cong\ \angle X$  

•  $\angle T\ \cong\ \angle Z$  

•  $\overline{RT}\ \cong\ \overline{XZ}$  

•  $\overline{SR}\ \cong\ \overline{YZ}$  

 $\Delta ABC\ \cong\ \Delta DEF$  ,  $m\angle A\ =\ 50\degree,$  and  $m\angle E\ =\ 30\degree.$  What is  $m\angle C$  ?

•  $50\degree$  

•  $30\degree$  

•  $80\degree$  

•  $100\degree$  

 $\Delta ABC\ \cong\ \Delta EDC$  by

• SSS

• SAS

• ASA

• AAS

 $\Delta WXZ\ \cong\ \Delta YZX$  by

• SSS

• SAS

• ASA

• AAS

What additional information do you need to prove that
 $\Delta GHI\ \cong\ \Delta DEF$  

•  $\overline{HI}\ \cong\ \overline{EF}$  

•  $\angle F\ \cong\angle G$  

•  $\overline{HI}\ \cong\ \overline{ED}$  

•  $\overline{GI}\ \cong\ \overline{DF}$  

What additional information do you need to prove that
 $\Delta NOP\ \cong\ \Delta QSR$  

•  $\overline{PN}\ \cong\ \overline{SQ}$  

•  $\angle P\ \cong\ \angle S$  

•  $\angle O\ \cong\ \angle S$  

•  $\overline{NO}\ \cong\ \overline{QR}$