document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210506>Question 1210506</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What kind of quadrilateral has the property that both pairs of opposite sides are parallel?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that all four sides are equal in length?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that all four angles are right angles?   Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that all four sides are equal in length and all four angles are right angles?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that exactly one pair of opposite sides is parallel?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that its diagonals bisect each other?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that its diagonals are congruent (equal in length)?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that its diagonals are perpendicular bisectors of each other?   Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that its diagonals are perpendicular?   Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that all vertices lie on a single circle (cyclic quadrilateral)?    Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that it is a trapezoid, and the two non-parallel sides (legs) are equal in length?   Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that the sum of the measures of its consecutive angles is $180^\circ$?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that the diagonals of the quadrilateral always divide it into four congruent triangles of equal area?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that two pairs of adjacent sides are equal in length, but all four sides are not equal?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that the lengths of its diagonals are equal, and the diagonals are perpendicular?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that the distance between the two parallel sides is constant? (This is a more descriptive property for a specific type).  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that its diagonals bisect the interior angles?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that it is a rectangle, but it is not a square?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that its diagonals are congruent and bisect each other, but they are not perpendicular?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that its opposite angles are congruent?  Select all that apply.\r<BR>\n" );
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document.write( "What kind of quadrilateral has the property that the segments connecting the midpoints of its consecutive sides form a rhombus?   Select all that apply. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #853072 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2141)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=853072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a great set of questions about the properties of different quadrilaterals!\r<BR>\n" );
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document.write( "Here are the answers, with a brief explanation and an image tag for a visual aid.\r<BR>\n" );
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document.write( "### 📐 Quadrilateral Properties\r<BR>\n" );
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document.write( "| Property | Quadrilateral Type |<BR>\n" );
document.write( "| :--- | :--- |<BR>\n" );
document.write( "| **Both pairs of opposite sides are parallel.** | * **Parallelogram** * **Rectangle** * **Rhombus** * **Square** |<BR>\n" );
document.write( "| **All four sides are equal in length.** | * **Rhombus** * **Square** |<BR>\n" );
document.write( "| **All four angles are right angles.** | * **Rectangle** * **Square** |<BR>\n" );
document.write( "| **All four sides are equal in length AND all four angles are right angles.** | * **Square** |<BR>\n" );
document.write( "| **Exactly one pair of opposite sides is parallel.** | * **Trapezoid** (or **Trapezium** in some regions) |<BR>\n" );
document.write( "| **Its diagonals bisect each other.** | * **Parallelogram** * **Rectangle** * **Rhombus** * **Square** |<BR>\n" );
document.write( "| **Its diagonals are congruent (equal in length).** | * **Rectangle** * **Square** * **Isosceles Trapezoid** |<BR>\n" );
document.write( "| **Its diagonals are perpendicular bisectors of each other.** | * **Rhombus** * **Square** |<BR>\n" );
document.write( "| **Its diagonals are perpendicular.** | * **Rhombus** * **Square** * **Kite** |\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### **Detailed Notes on Relationships**\r<BR>\n" );
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document.write( "* **Parallelogram:** A quadrilateral with two pairs of parallel sides. All parallelograms have diagonals that bisect each other.<BR>\n" );
document.write( "* **Rectangle:** A parallelogram with four right angles. It inherits all parallelogram properties (including diagonals bisecting each other) and adds the property of having congruent diagonals.<BR>\n" );
document.write( "* **Rhombus:** A parallelogram with four equal sides. It inherits all parallelogram properties and adds the property of having perpendicular diagonals that are also perpendicular bisectors.<BR>\n" );
document.write( "* **Square:** A quadrilateral that is *both* a Rectangle and a Rhombus. It has all the properties listed for both, including four equal sides, four right angles, parallel opposite sides, and diagonals that are congruent, perpendicular, and bisect each other.<BR>\n" );
document.write( "* **Trapezoid:** Has exactly one pair of parallel sides.<BR>\n" );
document.write( "* **Kite:** Has two distinct pairs of equal-length adjacent sides. Its diagonals are perpendicular.\r<BR>\n" );
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document.write( "Would you like to explore the properties of a specific quadrilateral in more detail, like the kite or an isosceles trapezoid? </SPAN>\n" );
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