rhombuses, rectangles, & squares sec 6.4 continued goals: to use properties of diagonals for the...

Rhombuses, Rectangles, & Squares Sec 6.4 Continued GOALS: To use properties of diagonals for the rhombus, rectangle, and square

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Rhombuses, Rectangles, & Squares

Sec 6.4 Continued

GOALS:To use properties of diagonals for the rhombus, rectangle, and square

Theorem 6.11A parallelogram is a rhombus if and only if its diagonals

are perpendicular.

W X

WXYZ is a rhombus if and only if ZX WY

Page 3: Rhombuses, Rectangles, & Squares Sec 6.4 Continued GOALS: To use properties of diagonals for the rhombus, rectangle, and square

Theorem 6.12A parallelogram is a rhombus if and only if each diagonal

bisects a pair of opposite angles.

W X

bisects YZW & WXY and

bisects ZWX & XYZ

WXYZ is a rhombus if and only if

W X

Page 4: Rhombuses, Rectangles, & Squares Sec 6.4 Continued GOALS: To use properties of diagonals for the rhombus, rectangle, and square

Theorem 6.13

W X

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

WXYZ is a rectangle if and only if

ZX WY

Page 5: Rhombuses, Rectangles, & Squares Sec 6.4 Continued GOALS: To use properties of diagonals for the rhombus, rectangle, and square

Example PQRS is a parallelogram.Find x

S R

2x10

Page 6: Rhombuses, Rectangles, & Squares Sec 6.4 Continued GOALS: To use properties of diagonals for the rhombus, rectangle, and square

Example PQRS is a rhombus.Find x

S R

Page 7: Rhombuses, Rectangles, & Squares Sec 6.4 Continued GOALS: To use properties of diagonals for the rhombus, rectangle, and square

Example

W X

WXYZ is a rectangle. The perimeter is triangle XYZ is 24.

XY+YZ = 5x+1 and XZ = 13-x. Find WY.

Page 8: Rhombuses, Rectangles, & Squares Sec 6.4 Continued GOALS: To use properties of diagonals for the rhombus, rectangle, and square

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