Geo 6.4 Properties of Special Parallelograms PPT

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Transcript Geo 6.4 Properties of Special Parallelograms PPT

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.
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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.
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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.
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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.
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6-4 Properties of Special Parallelograms
Lesson Quiz: Part IV
6. Given: ABCD is a rhombus.
Prove: ABE  CDF

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