6.5 Rhombi and Squares - Ms. Fowls' Math Classes
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Transcript 6.5 Rhombi and Squares - Ms. Fowls' Math Classes
6.5 Rhombi and Squares
Rhombus
Quad with 4 sides
Rhombus
Theorem 6.15: The diagonals
of a rhombus are .
Theorem 6.16: If the
diagonals of a parallelogram
are , then the parallelogram
is a rhombus.
Theorem 6.17: Each
diagonal of a rhombus bisects
a pair of opposite angles.
All 4 of the s are .
Example
Refer to Example #2 picture on page 349
Do Check Your Progress #2
Answer:
114
Square
Both a rhombus and a rectangle
All sides are
All angles are right angles (90°)
Quadrilaterals
Parallelograms
Rhombi
Squares
Rectangles
Example
Given the vertices J(5,0), K(8, -11), L (-3,-14), M(6,-3), determine whether parallelogram JKLM is a
rhombus, a rectangle, or a square. List all that apply.
Use the distance formula to compare the lengths of
the diagonals. Use the slope formula to determine if
the sides are perpendicular.
Answer: Square, rectangle, and rhombus, all sides
are congruent and perpendicular.
Summaries
Rhombus Properties
Opposites sides are
Opposite angles are
Consecutive angles are
supplementary.
Diagonals bisect each other
Diagonals are perpendicular
Each diagonal bisects two angles.
4 sides are
Square Properties
Opposites sides are
Opposite angles are
Consecutive angles are
supplementary.
Diagonals bisect each other
Diagonals are perpendicular
Each diagonal bisects two angles.
All four angles are right angles.
Diagonals are
4 sides are
Homework #40
p. 352 11, 15-18, 19-25 odd, 31-34