Lin wrote a proof to show that diagonal is a line of symmetry for rhombus . Fill in the blanks to complete her proof. 

Because is a rhombus, the distance from to is the same as the distance from to . Since is the same distance from as it is from , it must lie on the perpendicular bisector of segment . By the same reasoning, must lie on the perpendicular bisector of . Therefore, line is the perpendicular bisector of segment . So reflecting rhombus across line will take to and to (because and are on the line of reflection) and to and to (since is perpendicular to the line of reflection, and and are the same distance from the line of reflection, on opposite sides). Since the image of rhombus reflected across is rhombus (the same rhombus!), line must be a line of symmetry for rhombus .

In quadrilateral , is congruent to , and is parallel to . Andre has written a proof to show that is a parallelogram. Fill in the blanks to complete the proof. 

Since is parallel to , alternate interior angles  and  are congruent. is congruent to  since segments are congruent to themselves. Along with the given information that is congruent to , triangle is congruent to  by the  Triangle Congruence Theorem. Since the triangles are congruent, all pairs of corresponding angles are congruent, so angle is congruent to . Since those alternate interior angles are congruent, must be parallel to . Since we define a parallelogram as a quadrilateral with both pairs of opposite sides parallel, is a parallelogram. 

Select the statement that must be true.

Figure  is a parallelogram. Is triangle  congruent to triangle ? Show or explain your reasoning.

Figure  is a parallelogram. Prove that triangle  is congruent to triangle .