geometry/notes 8.5
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Rhombi & SquaresSECTION 8.5
What are the properties of a rhombus, and how do I apply them?
What are the properties of squares, and how do I apply them?
Rhombi is plural of rhombus
RHOMBI AND SQUARES
Rhombus: A quadrilateral with all four sides congruent.
How does this compare to a parallelogram?
RHOMBUS
All properties of a parallelogram apply, so…
1. Opposite Sides are and 2. Opposite s are 3. Consecutive s are supplementary4. Diagonals bisect each other
New
5. Diagonals are perpendicular to each other6. Diagonals bisect opposite angles
PROPERTIES
Square – A quadrilateral that is a rhombus and rectangle.
SQUARE
All properties of a parallelogram and rectangle apply, so…
1. All Sides are 2. All s are (90°)3. Diagonals are 4. Diagonals bisect each other5. Diagonals are perpendicular to each other6. Diagonals bisect opposite angles
PROPERTIES OF A SQUARE
Use rhombus LMNP to find the value of y if m
EXAMPLE
N
In rhombus LMNP, MN = 2x + 3 and NP = 5x. Find x and MN.
EXAMPLE
N
Use rhombus LMNP to find m
EXAMPLE
N
Use rhombus ABCD and the given information to find the value of each variable.
Find
Find
EXAMPLE
E
Determine whether parallelogram EFGH is a rhombus, a rectangle or a square for E(0,-2), F(-3, 0), G(-1, 3) and H(2, 1). List all that apply. Explain.
EXAMPLE
Page 434 12 – 19 20 – 30 (Even) Skip 24!
Hint on #12 – a quadrilateral has 360°, so add up the four angles
HOMEWORK