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6.4 Special Parallelograms

6.4 Special Parallelograms. Chapter 6 Quadrilaterals. 6.4 Special Parallelograms. Theorem 6.9 Each diagonal of a rhombus bisects two angles of the rhombus. 2. 1. <1 = < 2 and < 3 = <4. <1 = < 3 and < 2 = <4 Because they are isosceles triangles, So <1 = <2 = <3 = <4. 4. 3.

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6.4 Special Parallelograms

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  1. 6.4 SpecialParallelograms Chapter 6 Quadrilaterals

  2. 6.4 Special Parallelograms • Theorem 6.9 Each diagonal of a rhombus bisects two angles of the rhombus. 2 1 <1 = < 2 and < 3 = <4 <1 = < 3 and < 2 = <4 Because they are isosceles triangles, So <1 = <2 = <3 = <4 4 3

  3. 6.4 Special Parallelograms • Theorem 6-10 The diagonals of a rhombus are perpendicular A B AC ┴ DB D C

  4. Finding Angle Measure • MNPQ is a rhombus and m<N =120°. Find the measures of the numbered angles. N P 3 120° 4 1 2 M Q

  5. Finding Angles Measures • Find the measures of the numbered angles in the rhombus. m<1 : m<2 and m<3: 50° 1 m<4: 3 4 2

  6. 6.4 Special Parallelograms • Theorem 6-11 The diagonals of a rectangle are congruent

  7. Finding Diagonal Length • Find the length of the diagonals of rectangle GFED if FD = 2y + 4 and GE = 6y – 5. G F E D

  8. Is the Parallelogram a Rhombus or a Rectangle? • Theorem 6-12 If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus. • Theorem 6-13 If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. • Theorem 6-14 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

  9. Practice: • Pg 315 1-21, 48-50

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