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6.4 Rhombuses, Rectangles, and Squares

6.4 Rhombuses, Rectangles, and Squares. Advanced Geometry. Properties of Parallelograms. Write down 5 properties of parallelograms. RHOMBUS. A rhombus is a parallelogram with four congruent sides. RECTANGLE. A rectangle is a parallelogram with four right angles. SQUARE.

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6.4 Rhombuses, Rectangles, and Squares

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  1. 6.4 Rhombuses, Rectangles,and Squares Advanced Geometry

  2. Properties of Parallelograms Write down 5 properties of parallelograms.

  3. RHOMBUS A rhombus is a parallelogram with four congruent sides.

  4. RECTANGLE A rectangle is a parallelogram with four right angles.

  5. SQUARE A square is a parallelogram with four congruent sides and four right angles.

  6. Parallelograms

  7. Describing a Special Parallelogram Decide whether the statement is always, sometimes, or never true. • A rhombus is a rectangle • A parallelogram is a rectangle • A rectangle is a square • A square is a rhombus

  8. Corollaries about Special Quadrilaterals • Rhombus Corollary – A quadrilateral is a rhombus if and only if it has four congruent sides. • Rectangle Corollary – A quadrilateral is a rectangle if and only if it has four right angles. • Square Corollary – A quadrilateral is a square if and only if it is a rhombus and a rectangle.

  9. THEOREM 6.11 A parallelogram is a rhombus if and only if its diagonals are perpendicular.

  10. THEOREM 6.12 A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

  11. THEOREM 6.13 A parallelogram is a rectangle if and only if its diagonals are congruent.

  12. Example In parallelogram ABCD, the diagonals meet at point E, and AE = BE = 6. Is ABCD a rectangle?

  13. Example QRST is a square. What else do you know about QRST?

  14. Example EFGH is a rectangle. K is the midpoint of FH. If EG = 8z – 16, what is EK? GK?

  15. Example ABCD is a rectangle and measure of angle B = 8x + 26. What is the value of x?

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