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8-4: Rectangles, Rhombi, and Squares

8-4: Rectangles, Rhombi, and Squares. Oh my!. 8-4: Rectangles, Rhombi, and Squares. Quadrilateral. Parallelogram opposite sides parallel opposite sides congruent. Rhombus parallelogram with 4 congruent sides.

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8-4: Rectangles, Rhombi, and Squares

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  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 4 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

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