Exploring Properties of Parallelograms, Rhombuses, and Rectangles
Delve into the theorems and examples related to the properties of parallelograms, rhombuses, and rectangles. Understand concepts such as diagonals in rhombuses, perpendicular diagonals in parallelograms, and congruent diagonals in rectangles. Learn to identify these shapes based on specific criteria and explore the unique properties that define each geometric figure.
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6 6- -4 SPECIAL 4 SPECIAL PARALLELOGRAMS PARALLELOGRAMS GEOMETRY
Theorem 6-9: Each diagonal of a rhombus bisects two angles of the rhombus. 1 2 3 4 5 6 7 8
Theorem 6 Theorem 6- -10: perpendicular. perpendicular. 10: The diagonals of a rhombus are The diagonals of a rhombus are ?? ??
Example 1 Example 1
Example 2 Example 2
Theorem 6 Theorem 6- -11: are congruent. are congruent. 11: The diagonals of a rectangle The diagonals of a rectangle ?? ??
Example 3 Example 3
Identifying a Rhombus Identifying a Rhombus 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. Identifying a Rectangle Identifying a Rectangle Theorem 6-14: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Example 4 Example 4
Example 5 Example 5 Rhombus, Rectangle, or Neither? Rhombus, Rectangle, or Neither?
Property Parallelogram Rectangle Rhombus Square Opp. sides are parallel Opp. sides are congruent Opp. <'s are congruent One set of sides is congruent and parallel A diag. forms 2 congruent triangles Diags. bisect each other Diags. are congruent Diags. are perpendicular A diag. bisects two <'s All <'s are right <'s All sides are congruent
