8 4 Rectangles Rhombi and Squares Oh my

8 -4: Rectangles, Rhombi, and Squares Oh my!

8 -4: Rectangles, Rhombi, and Squares Quadrilateral Parallelogram opposite sides parallel opposite sides congruent Rectangle parallelogram with 4 right angles Rhombus parallelogram with 4 congruent sides Square parallelogram with 4 congruent sides and 4 right angles

8 -4: Rectangles, Rhombi, and Squares In 8 -2, we learned that in a parallelogram, the diagonals bisect each other. With these new shapes, we get a couple of new theorems about their diagonals. Theorem 8 -10: The diagonals of a rectangle are congruent. AC = BD

8 -4: Rectangles, Rhombi, and Squares Theorem 8 -11: The diagonals of a rhombus are perpendicular. AC BD Theorem 8 -12: The diagonals of a rhombus bisect a pair of opposite angles 1 3 5 7 = = 2 4 6 8

8 -4: Rectangles, Rhombi, and Squares Find XZ in square XYZW if YW = 14 Since a square is also a rectangle, the diagonals of a square (rectangle) are congruent. XZ = 14 Find m YOX in square XYZW Since a square is also a rhombus, the diagonals of a square (rhombus) are perpendicular m YOX = 90

8 -4: Rectangles, Rhombi, and Squares YOUR TURN Name all segments that are congruent to WO in square XYZW YO, OZ, and OX Name all angles congruent to XYO in square XYZW ZYO (diagonals bisect) YZO, WZO (all vertex angles congruent) ZWO, XWO WXO, YXO

8 -4: Rectangles, Rhombi, and Squares Assignment Worksheet 8 -4