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Rhombi and Squares

Rhombi and Squares. Section 6.5. Rhombus or plural is Rhombi. A quadrilateral with all 4 sides congruent Properties: 1. Diagonals are perpendicular 2. Each diagonal bisects a pair of opposite angles. Square. A quadrilateral with four right angles and four congruent sides Properties:

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Rhombi and Squares

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  1. Rhombi and Squares Section 6.5

  2. Rhombus or plural is Rhombi • A quadrilateral with all 4 sides congruent • Properties: • 1. Diagonals are perpendicular • 2. Each diagonal bisects a pair of opposite angles

  3. Square • A quadrilateral with four right angles and four congruent sides • Properties: • 1. All properties of parallelograms apply • AND • 2. All properties of rectangle apply • AND • 3. All properties of a rhombus apply

  4. Examples • ABCD is a rhombus • 1. If m <ABD = 60, • Find m<DBC. • ANS: 60 • 2. If AE = 8, find AC. • ANS: 16 • 3. If AB = 26 and BD = 20, find AE. • ANS: 24

  5. 4. Find m<CEB. • ANS: 90 • 5. If m<CBD = 58, • Find m<ACB. • ANS: 32 • 6. If AE = 3x – 1 and AC = 16, find x • ANS: 3 • 7. If m<CDB = 6y and m<ACB = 2y + 10, find y. • ANS: 10

  6. If given four ordered pairs and asked to decide what shape the quadrilateral is: • 1. Check the slope of the opposite sides to see if it is a parallelogram. • 2. If it is a parallelogram check the slope of the consecutive sides to see if it is a rectangle. • 3. If the sides are perpendicular, then it may be a square or rectangle so check the side lengths.

  7. 4. If all four sides are congruent it is a square, if only the 2 pairs of opposite sides are congruent then it is a rectangle. • 5. If sides are parallel but no right angles, it must be a rhombus.

  8. Determine whether the given vertices represent a parallelogram, rectangle, rhombus, or square. Explain • A(1, 3) B(7, -3) C(1, -9) D(-5, -3) • Step 1 Graph the ordered pairs. • Step 2: Find the slope of all four sides • Step 3: Find the length of all four sides.

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