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Rectangles, Squares, and Rhombi, Oh My!

Rectangles, Squares, and Rhombi, Oh My!. Notes. Rectangles, Squares, and Rhombi Are All Special Types of Parallelograms. Parallelogram. Rectangle. Rhombus. Square. All Have the Properties of Parallelograms. Opposite sides are parallel Opposite sides are congruent

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Rectangles, Squares, and Rhombi, Oh My!

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  1. Rectangles, Squares, and Rhombi, Oh My! Notes

  2. Rectangles, Squares, and Rhombi Are All Special Types of Parallelograms Parallelogram Rectangle Rhombus Square

  3. All Have the Properties of Parallelograms • Opposite sides are parallel • Opposite sides are congruent • Opposite angles are congruent • Consecutive angles are supplementary • Diagonals bisect each other 90+90=180

  4. Rectangles Also Have These Properties • All angles are right angles • Diagonals are congruent

  5. Rhombi Also Have These Properties • All four sides are congruent • Diagonals are perpendicular • Diagonals bisect opposite angles

  6. Squares Have All the Properties of Rectangles and Rhombi (and Parallelograms, too!) • All four sides are congruent • All four angles are right angles • Diagonals are congruent • Diagonals are perpendicular • Diagonals bisect opposite angles

  7. An Example With Rectangles Further explanation: If HF = 42, then EG = 42. (The diagonals are congruent.) If EG = 42, then EM = 21. (The diagonals bisect each other.) Therefore, 5x + 1 = 21 is the equation you can use to solve for x.

  8. An Example With A Rhombus Further explanation: The diagonal DB cuts angle D in half. (Diagonals bisect opposite angles.) One of those halves is angle ADB, and we are given that it is 27 degrees. That means the other half is also 27 degrees. This makes all of angle D equal to 27 + 27 = 54 degrees. Therefore, the measure of angle ADC is 54 degrees.

  9. A Graphing Example Further explanation: Graph the points. Connect the dots. Check the lengths of the sides. Check the angles. Since all sides are the same and all angles are right angles, this is a SQUARE. (But squares are also rectangles and rhombi which are also parallelograms….) ANSWER: parallelogram, rectangle, rhombus, and square.

  10. Now It’s Your Turn! Use the properties you have learned here and the examples you have studied in these notes to complete the Rectangles, Rhombi, and Squares Homework you have downloaded from the website. This homework is due at the beginning of the next class period.

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