1. 8-4: Rectangles, Rhombi, and Squares
Oh my!

2. 8-4: Rectangles, Rhombi, and Squares
Quadrilateral
Parallelogram opposite sides parallel
opposite sides congruent
Rhombus parallelogram with 4 congruent sides
Rectangle parallelogram with right angles
Square parallelogram with 4 congruent sides and 4 right angles

3. 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

4. 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 = 2 3 = 4 5 = 6 7 = 8

5. 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

6. 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

7. 8-4: Rectangles, Rhombi, and Squares
Assignment
Worksheet 8-4