Lesson PROPERTIES OF PARALLELOGRAMS

Source code of 'PROPERTIES OF PARALLELOGRAMS'

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<H2>PROPERTIES OF PARALLELOGRAMS</H2>

For your convenience, this file contains the annotations to my lessons on parallelograms in this site and the major properties of parallelograms. The properties 
are presented with the links to the corresponding lessons. The lessons are listed in the logical order, which means that every given lesson refers to the preceding ones 
and does not refer to that follow. The list consolidates the relevant lessons that are located under different topics in this site. 
At the end of the list there are links to the lessons on word problems related to parallelograms.
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The lesson title

<A HREF=http://www.algebra.com/algebra/homework/Parallelograms/In-a-parallelogram-each-diagonal-divides-it-in-two-congruent-triangles.lesson>In a parallelogram, each diagonal 
divides it in two congruent triangles</A>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

<A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Properties-of-the-sides-of-a-parallelogram.lesson>Properties of the sides of a parallelogram</A>

<A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Properties-of-the-sides-of-parallelograms.lesson>Properties of the sides of parallelograms</A>

<A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Properties-of-diagonals-of-parallelograms.lesson>Properties of diagonals of parallelograms</A>

<A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Opposite-angles-of-a-parallelogram-are-congruent.lesson>Opposite angles of a parallelogram</A>

<A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Consecutive-angles-of-a-parallelogram.lesson>Consecutive angles of a parallelogram</A>

The lesson title

<A HREF=http://www.algebra.com/algebra/homework/word/geometry/Midpoints-of-a-quadrilateral-are-vertices-of-the-parallelogram.lesson>Midpoints of a quadrilateral are vertices 
of the parallelogram</A>

<A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-length-of-diagonals-of-a-parallelogram.lesson>The length of diagonals of a parallelogram</A>

<A HREF=https://www.algebra.com/algebra/homework/Parallelograms/Remarcable-advanced-problems-on-parallelograms.lesson>Remarcable advanced problems on parallelograms</A>

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The property

In a parallelogram, each diagonal divides it&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
in two congruent triangles.

In a parallelogram, the opposite sides are of equal 
length in pairs.
If in a quadrilateral the opposite sides are of equal 
length in pairs, then the quadrilateral is a parallelogram.

If a quadrilateral has two opposite sides parallel 
and of equal length, then two other opposite sides 
are parallel and of equal length too.
If in a quadrilateral two opposite sides are parallel 
and two other opposite sides are parallel too, then 
the opposite sides of each pair are of equal length.

In a parallelogram, the two diagonals bisect each other.
If in a quadrilateral the two diagonals bisect each other, 
then the quadrilateral is a parallelogram.

In a parallelogram, the opposite angles are congruent. 
If in a convex quadrilateral the opposite angles are 
congruent, then the quadrilateral is a parallelogram.

In a parallelogram, the sum of any two consecutive  
angles is equal to 180�. 
If in a quadrilateral the sum of any two consecutive 
angles is equal to 180�, then the quadrilateral is 
a parallelogram.

The property

In a convex quadrilateral the midpoints of its sides 
are vertices of the parallelogram.

If a, b, c and d are the lengths of the sides of a parallelogram 
and {{{d[1]}}} and {{{d[2]}}} are the lengths of its diagonals, then 
{{{d[1]^2 + d[2]^2}}} = {{{a^2+b^2+c^2+d^2)/2}}} = {{{2a^2 + 2b^2}}}.

In a parallelogram the segments connecting the opposite 
vertices with the midpoints of the parallel sides cut 
the diagonal in three congruent parts.

In a parallelogram the lengths of the adjacent sides  are 
8 cm and 3 cm respectively. Angle bisectors drawn from the vertices 
of the long side split the opposite side into three segments. 
Find the length of each of these segments.

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Under the topic

Parallelograms&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

Parallelograms

Triangles

Parallelograms

Under the topic

Geometry

Parallelograms

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In the section&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

Geometry

In the section

Word problems

Geometry

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For the solutions of the typical word problems on parallelograms related to their sides and angles measures see the lessons
&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=http://www.algebra.com/algebra/homework/word/geometry/How-to-solve-problems-on-the-parallelogram-sides-measures-Examples.lesson>HOW TO solve problems on the parallelogram sides measures - Examples</A> and 
&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=http://www.algebra.com/algebra/homework/word/geometry/How-to-solve-problems-on-the-angles-of-parallelograms.lesson>HOW TO solve problems on the angles of parallelograms - Examples</A> 
under the topic Geometry of the section Word problems in this site.

To navigate over all topics/lessons of the Online Geometry Textbook use this file/link &nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A>.