# Master the Isosceles Trapezoid from recognition to construction. The Isosceles Trapezoid can sometimes cause quite a bit of confusion.  This is because people often refer to it as simply a Trapezoid, but as you will see from this page, even though it is a trapezoid, it has some extra special features making it an isosceles shape.

The seven steps detailed bellow take you from basic identification all the way through to taking a detailed look at the theorems involving the isosceles trapezoid.

These steps also include 'pit stops' to complete fun geometry projects and coloring sheets.

These are nice 'breathers' on the learning curve, but they are excellent ways of reinforcing the new knowledge in ways that your kid can get a real life, hands on approach to understanding the basic geometry concepts included.

Okay, so let's get started ... ## Identify - How do we know it's an Isosceles Trapezoid?

First and fore most it is a quadrilateral which is a 4 sided plane shape.

• It has 4 lines
• Two of the lines are parallel
• The other two lines are equal in length.
• The angles at its base are equal.
• The remaining two angles are equal.
• It is a Simple Quadrilateral (The sum of its angles is 360 degrees
• An Isosceles Trapezoid is also a Trapezoid

Once your child is comfortable with how to recognize the shape, offer them some shape worksheets to see how they get on with identifying the shape when compared with others.

You may also find our  Quadrilateral Family Tree Printable a useful tool to offer your child. ## Calculate Area & Perimeter of an Isosceles Trapezoid

#### Please note this is NOT a formula your K-6 grade student is required to know.These images are of a Trapezoid, but the formula for these two shapes are the same. The Area of this type of trapezoid is calculated by first getting the AVERAGE length of the two sides that are parallel.

Then you multiply this average by the altitude (height) of the shape.  If your child has problems understanding the concept of Area, I recommend working with second grade 'grid method' worksheets first, and then move on to fourth grade worksheets using numbers and finally word problems. The Perimeter of ANY shape is simply the sum total of all the lengths of the shape - and an isosceles trapezoid is no different. ## How to Construct an Isosceles Trapezoid

To complete this, you will need a ruler, pencil, compass and a blank piece of paper!

Note:  This construction is based upon having the knowledge of the height of the trapezoid along with the angles at its base.

Step 1: Draw a straight line lightly using your ruler and pencil on your paper. - This is what we call a construction line, and will be the base of your trapezoid.

Step 2: Indicate the two end points of the base of your shape with two points, measured by your ruler.

Note: We know that the top and base line of your trapezoid are parallel, and, we know the distance between them (the height of your shape).

Step 3: Using your compass, construct two lines (lightly) perpendicular to your base. On both of these lines measure the height of your trapezoid, and indicate with two points (one on each perpendicular).  Connect these two points using a light construction line. The second side of your trapezoid will be 'somewhere' on this line.

Step 4: Using your protractor, measure the angles at the base, using the points on your first construction line and construct your third and fourth sides.

Note:  You will now have four construction lines, intersecting at four vertices.

Step 5: Your isosceles trapezoid is the shape contained between the four points of intersection of these four lines.

Step 6: Using a heavier line connect the four points to finish your shape.   ## Relationship to 3D Shapes

There are no 3D Figures a Kindergarten through Sixth grade student is expected to study in relation to this shape. ## Geometric Coloring Sheets

The use of coloring sheets allows your child to start experimenting with triangles.  A great first step is to encourage your child to color in triangles adjacent to each other with the same color, until their shape starts to look like 'something'.

Perhaps that something will be a rectangle or a house! By doing this, your child will start to realize the connection between different shapes.  You will find some nice free geometric coloring pages to download and get started with. ## Fun Geometry Projects

Coming soon! Pythagoras

Coming soon!