Download 7-4 Special Parallelogram

7-4 Properties of Special Parallelograms
6-4
Leaning Objectives
To learn about the properties of
rectangles, rhombuses, and squares
and to apply them while solving
problems.
Holt Geometry
7-4 Properties of Special Parallelograms
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Vocabulary
Holt Geometry
7-4 Properties of Special Parallelograms
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A rectangle is another special quadrilateral.
A rectangle is a quadrilateral with four right angles.
Holt Geometry
7-4 Properties of Special Parallelograms
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Since a rectangle is a parallelogram, a rectangle
“inherits” all the properties of parallelograms.
Holt Geometry
7-4 Properties of Special Parallelograms
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Example 1
A rectangular: JK = 50 cm and
JL = 86 cm. Find HM.
Holt Geometry
7-4 Properties of Special Parallelograms
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Example 2
The rectangular gate has
diagonal braces. Find HJ.
Holt Geometry
7-4 Properties of Special Parallelograms
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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
7-4 Properties of Special Parallelograms
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Holt Geometry
7-4 Properties of Special Parallelograms
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Example 3:
TVWX is a rhombus.
Find TV.
Holt Geometry
7-4 Properties of Special Parallelograms
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Example 4:
TVWX is a rhombus.
Find mVTZ.
Holt Geometry
7-4 Properties of Special Parallelograms
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Example 5
CDFG is a rhombus.
Find CD.
Holt Geometry
7-4 Properties of Special Parallelograms
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Example 6
CDFG is a rhombus.
Find the measure.
mGCH if mGCD = (b + 3)°
and mCDF = (6b – 40)°
Holt Geometry
7-4 Properties of Special Parallelograms
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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
7-4 Properties of Special Parallelograms
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Helpful Hint
Rectangles, rhombuses, and squares
are sometimes referred to as special
parallelograms.
Holt Geometry
7-4 Properties of Special Parallelograms
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Example 7: Verifying Properties of Squares
Show that the diagonals of
square EFGH are congruent
perpendicular bisectors of
each other.
Holt Geometry
7-4 Properties of Special Parallelograms
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Example 8
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
7-4 Properties of Special Parallelograms
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Example 9
Holt Geometry
7-4 Properties of Special Parallelograms
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Example 10
In rectangle CNRT, CN = 35 ft, and NT = 58
ft. Find each length.
1. TR
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2. CE
7-4 Properties of Special Parallelograms
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Example 11
PQRS is a rhombus. Find each measure.
3. QP
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4. mQRP
7-4 Properties of Special Parallelograms
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Example 12
Classify the special quadrilateral.
Holt Geometry
7-4 Properties of Special Parallelograms
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Example 13
Find the measures of the numbered
angles in Rhombus DEFG.
Holt Geometry
7-4 Properties of Special Parallelograms
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What is the m
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Example 14
ADC and m BCD?
7-4 Properties of Special Parallelograms
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Example 15
Find the measures of the numbered angles in
rhombus ABCD.
Holt Geometry
7-4 Properties of Special Parallelograms
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Holt Geometry