1 Objectives State the properties of rectangles, rhombuses, and squares Solve problems involving rectangles, rhombuses, and squares

2 Diagonals of Rhombus Bisect Angles A parallelogram is a rhombus if and only if each diagonal bisects two angles of the rhombus. –∠1 ≅ ∠2 and ∠3 ≅ ∠4 –Since ∠BCD and ∠BAD are opposite angles of a parallelogram, ∠1 ≅ ∠2 ≅ ∠3 ≅ ∠4

3 Diagonals of a Rhombus are Perpendicular A parallelogram is a rhombus if and only if the diagonals are perpendicular.

4 Diagonals of a Rectangle A parallelogram is a rectangle if and only if the diagonals are congruent.

5 Squares A square is a parallelogram, rectangle, and rhombus. All properties of parallelograms, rectangles, and rhombi apply to squares

6 Example: Rhombus Find m ∠XTZ We need to solve for a before we can find m ∠XTZ. 14a + 20 = 90 ( diagonals of a rhombus are perpendicular ) 14a = 70 a = 5 5a – 5 = 20° ( substituting a = 5 in order to find m ∠XTZ )

7 Example: Rectangle Find FD in rectangle FEDG if FD = 2y + 4 and GE = 6y – 5 6y – 5 = 2y + 4 4y – 5 = 4 4y = 9 y = 9/4 FD = 2y + 4 = 2(9/4) + 4 = 8.5

8 Example: Square Show that the figure is a square. –Strategy: Show that the diagonals are perpendicular (rhombus) Show that the diagonals are congruent (rectangle) Since, Since EG = FH,