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constructions in geometry a la shmoop some people are happy being famous even [Woman walking down red carpet]

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with all the bad press they get some people like helping others and making a

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difference in the world regardless of how much money they earn and some people

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find true inner peace just by sitting on top of a construction scaffolding with [Man on top of crane]

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hard hats and day-old turkey sandwich of course construction isn't all about

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hammering up drywall and playing with power tools it's also about being

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creative in geometry a construction is a drawing that you make using only a

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straightedge a compass and a pencil a straightedge is anything you can use to

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make a straight line like a ruler or the back of your geometry textbook or a

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two-by-four a compass might point north if you're venturing through the Amazon [Person checks compass in Amazon rainforest]

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but in geometry we're talking about this thing which preserves distance and draws

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a perfect circle make sure to pack the right compass next time you're going on

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safari we use a pencil because well mistakes happen and whiteout is really

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expensive using only these three tools we can

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construct practically anything a perpendicular bisector a congruent angle

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an equilateral triangle or parallel lines let's try a relatively simple

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construction how do we construct an angle congruent to this given angle [Angle appears]

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we'll start by drawing array which will be one of the sides of our new angle now

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we can use our compass to mark an arc length within the given angle with the

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centre at the endpoint of the angle without changing the measurement of the

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compass let's draw an identical arc on our ray we adjust our compass to be the

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distance between the intersections between the arc and the sides of the [Person uses compass to mark an arc on the angle]

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given angle if we take this distance and apply it to the intersection between the

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arc and the ray we can draw a small arc that intersects with the

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two points are enough to draw another ray from the endpoint of the angle

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through the point where the two arcs intersect and there you have it a

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congruent angle constructed using only a pencil a straightedge and a compass it's [Construction worker holding a ruler, pencil and compass]

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no Eiffel Tower but it'll do

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