In this Cyberchase video segment, Matt and Jackie must figure out how to construct rectangular lids that match the size of two boxes precisely. They enlist the carpentry skills of one of the Three Little Pigs, who shows them how to use different tools to accurately measure the rectangular lids. For the first box, Jackie finds that she can easily trace the box to make a lid that fits perfectly. The second box cannot be traced, so Matt and Jackie decide to measure the sides of the box and then use the measurements to cut a rectangle of equal size out of a piece of Herculanium.
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Replicating a shape can be done in different ways, depending on the characteristics of the shape and the tools available. Tracing the outline of a shape is an easy way to know that you have created an exact match. You can use this technique with a pattern to cut fabric for a project such as a pillow or dress. Using a pattern makes it easy to create multiple objects without using measuring tools each time. You can use similar tools like a stencil or a cookie cutter to create duplicate shapes. For larger shapes, however, these techniques may be insufficient.
Sometimes it is necessary to take measurements to create an exact match. To start, it is necessary to note the characteristics of the shape, such as the lengths of the sides and the measure of the angles between adjacent sides. It is possible to use width and length measurements to create a parallelogram that is not a rectangle. Therefore, the fact that each of the four angles of a rectangle is ninety degrees is an important detail needed to produce an exact match.
It is worth noting that all rectangles are parallelograms, but not all parallelograms are rectangles. Squares are rectangles (and parallelograms), but they also have the special feature of four congruent sides and four 90-degree angles. There are several tools that can be used to create right angles: two include a carpenter's square and a protractor. Mathematical formulas provide another way to verify that an angle is a right angle. If you create a triangle by joining the two sides that comprise the angle, you can check whether the sum of the squares of the two sides is equal to the square of the hypotenuse (the side opposite the right angle). If it is, then the angle is a right angle. This is the converse of Pythagorean's Theorem.
The need for taking measurements arises often in daily life. For example, it is not practical to trace a large window and then bring that piece of paper into the store to buy blinds. Instead, it is more efficient to measure the exact width and height of the window and give these measurements to a store employee before they cut the blinds.
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