91Ó°ÊÓ

PROVING A THEOREM In Exercises 73 and 74 , write a proof for part of the Rhombus Opposite Angles Theorem (Theorem 7.12\()\) . Given PQRS is a parallelogram. \(\overline{\mathrm{PR}}\) bisects \(\angle \mathrm{SPQ}\) and \(\angle \mathrm{QRS}\) \(\mathrm{SQ}\) bisects \(\angle \mathrm{PSR}\) and \(\angle \mathrm{RQP}\) . Prove \(\quad \mathrm{PQRS}\) is a rhombus.

ABSTRACT REASONING Will a diagonal of a square ever divide the square into two equilateral triangles? Explain your reasoning.

ABSTRACT REASONING Will a diagonal of a rhombus ever divide the rhombus into two equilateral triangles? Explain your reasoning.

CRITICAL THINKING Which quadrilateral could be called a regular quadrilateral? Explain your reasoning.

REASONING Are all rhombuses similar? Are all squares similar? Explain your reasoning.

MAKING AN ARGUMENT Your friend claims a rhombus will never have congruent diagonals because it would have to be a rectangle. Is your friend correct? Explain your reasoning.