Use properties of special quadrilaterals

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EXAMPLE 1
Use properties of special quadrilaterals
For any rhombus QRST, decide whether the
statement is always or sometimes true. Draw a
sketch and explain your reasoning.
SOLUTION
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EXAMPLE 1
Use properties of special quadrilaterals
For any rhombus QRST, decide whether the
statement is always or sometimes true. Draw a
sketch and explain your reasoning.
SOLUTION
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EXAMPLE 2
Classify special quadrilaterals
SOLUTION
The quadrilateral has four congruent sides. One
of the angles is not a right angle, so the
rhombus is not also a square. By the Rhombus
Corollary, the quadrilateral is a rhombus.
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for Examples 1 and 2
GUIDED PRACTICE
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for Examples 1 and 2
GUIDED PRACTICE
2. A quadrilateral has four congruent sides
and four congruent angles. Sketch the
quadrilateral and classify it.
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EXAMPLE 3
List properties of special parallelograms
Sketch rectangle ABCD. List everything that you
know about it.
SOLUTION
By definition, you need to draw a figure with the
following properties
The figure is a parallelogram.
The figure has four right angles.
Because ABCD is a parallelogram, it also has
these properties
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EXAMPLE 3
List properties of special parallelograms
Opposite sides are parallel and congruent.
Opposite angles are congruent. Consecutive
angles are supplementary.
Diagonals bisect each other.
By Theorem 8.13, the diagonals of ABCD are
congruent.
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for Example 3
GUIDED PRACTICE
3. Sketch square PQRS. List everything you
know about the square.
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Homework 537 3-17, 19-24, 27-51 odd