ofofSpecial
Parallelograms
6-4
6-4 Properties
Properties
Special
Parallelograms
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
Holt
Geometry
6-4 Properties of Special Parallelograms
Do Now
Solve for x.
1. 16x – 3 = 12x + 13
2. 2x – 4 = 90
ABCD is a parallelogram. Find each
measure.
3. CD
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4. mC
6-4 Properties of Special Parallelograms
Objectives
TSW prove and apply properties of
rectangles, rhombuses, and squares.
TSW use properties of rectangles,
rhombuses, and squares to solve
problems.
Holt Geometry
6-4 Properties of Special Parallelograms
Vocabulary
rectangle
rhombus
square
Holt Geometry
6-4 Properties of Special Parallelograms
A second type of special quadrilateral is a rectangle.
A rectangle is a quadrilateral with four right angles.
Holt Geometry
6-4 Properties of Special Parallelograms
Since a rectangle is a parallelogram, a rectangle
“inherits” all the properties of parallelograms.
Holt Geometry
6-4 Properties of Special Parallelograms
Example 1: Craft Application
A woodworker constructs a
rectangular picture frame so
that JK = 50 cm and JL = 86
cm. Find HM.
Holt Geometry
6-4 Properties of Special Parallelograms
Example 2
Carpentry The rectangular gate
has diagonal braces.
Find HJ.
Holt Geometry
6-4 Properties of Special Parallelograms
Example 3
Carpentry The rectangular gate
has diagonal braces.
Find HK.
Holt Geometry
6-4 Properties of Special Parallelograms
A rhombus is another special quadrilateral. A
rhombus is a quadrilateral with four congruent
sides.
Like a rectangle, a rhombus is a parallelogram. So you
can apply the properties of parallelograms to
rhombuses.
Holt Geometry
6-4 Properties of Special Parallelograms
Holt Geometry
6-4 Properties of Special Parallelograms
Example 4: Using Properties of Rhombuses to Find
Measures
TVWX is a rhombus.
Find TV.
Holt Geometry
6-4 Properties of Special Parallelograms
Example 5: Using Properties of Rhombuses to Find
Measures
TVWX is a rhombus.
Find mVTZ.
Holt Geometry
6-4 Properties of Special Parallelograms
Example 6
CDFG is a rhombus.
Find CD.
Holt Geometry
6-4 Properties of Special Parallelograms
Example 7
CDFG is a rhombus.
Find the measure.
mGCH if mGCD = (b + 3)°
and mCDF = (6b – 40)°
Holt Geometry
6-4 Properties of Special Parallelograms
A square is a quadrilateral with four right angles and
four congruent sides. A square is a parallelogram, a
rectangle, and a rhombus. So a square has the
properties of all three.
Holt Geometry
6-4 Properties of Special Parallelograms
Helpful Hint
Rectangles, rhombuses, and squares are
sometimes referred to as special parallelograms.
Holt Geometry
6-4 Properties of Special Parallelograms
Example 8: Verifying Properties of Squares
Show that the diagonals of
square EFGH are congruent
perpendicular bisectors of
each other.
Holt Geometry
6-4 Properties of Special Parallelograms
Holt Geometry
6-4 Properties of Special Parallelograms
Example 9
The vertices of square STVW are S(–5, –4),
T(0, 2), V(6, –3) , and W(1, –9) . Show that
the diagonals of square STVW are congruent
perpendicular bisectors of each other.
Holt Geometry
6-4 Properties of Special Parallelograms
Holt Geometry
6-4 Properties of Special Parallelograms
Holt Geometry
6-4 Properties of Special Parallelograms
Holt Geometry
6-4 Properties of Special Parallelograms
Lesson Quiz: Part I
A slab of concrete is poured with diagonal
spacers. In rectangle CNRT, CN = 35 ft, and
NT = 58 ft. Find each length.
1. TR 35 ft
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2. CE 29 ft
6-4 Properties of Special Parallelograms
Lesson Quiz: Part II
PQRS is a rhombus. Find each measure.
3. QP
42
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4. mQRP
51°
6-4 Properties of Special Parallelograms
Lesson Quiz: Part III
5. The vertices of square ABCD are A(1, 3),
B(3, 2), C(4, 4), and D(2, 5). Show that its
diagonals are congruent perpendicular
bisectors of each other.
Holt Geometry
6-4 Properties of Special Parallelograms
Lesson Quiz: Part IV
6. Given: ABCD is a rhombus.
Prove: ABE  CDF

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