Rhombi and Squares
Section 6.5
Rhombus or plural is Rhombi
• A quadrilateral with all 4 sides congruent
• Properties:
• 1. Diagonals are perpendicular
• 2. Each diagonal bisects a pair of opposite
angles
Square
• A quadrilateral with four right angles and four
congruent sides
• Properties:
• 1. All properties of parallelograms apply
• AND
• 2. All properties of rectangle apply
• AND
• 3. All properties of a rhombus apply
Examples
•
ABCD is a rhombus
•
1. If m <ABD = 60,
•
Find m<DBC.
•
ANS: 60
•
2. If AE = 8, find AC.
•
ANS: 16
•
3. If AB = 26 and BD = 20, find AE.
•
ANS: 24
•
4. Find m<CEB.
•
ANS: 90
•
5. If m<CBD = 58,
•
Find m<ACB.
•
ANS: 32
•
6. If AE = 3x – 1 and AC = 16, find x
•
ANS: 3
•
7. If m<CDB = 6y and m<ACB = 2y + 10, find y.
•
ANS: 10
If given four ordered pairs and asked to
decide what shape the quadrilateral is:
• 1. Check the slope of the opposite sides to
see if it is a parallelogram.
• 2. If it is a parallelogram check the slope of
the consecutive sides to see if it is a rectangle.
• 3. If the sides are perpendicular, then it may
be a square or rectangle so check the side
lengths.
• 4. If all four sides are congruent it is a square, if
only the 2 pairs of opposite sides are congruent then
it is a rectangle.
• 5. If sides are parallel but no right angles, it must be
a rhombus.
• Determine whether the given vertices
represent a parallelogram, rectangle, rhombus,
or square. Explain
• A(1, 3) B(7, -3) C(1, -9) D(-5, -3)
• Step 1 Graph the ordered pairs.
• Step 2: Find the slope of all four sides
• Step 3: Find the length of all four sides.