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Description:

No hard hat needed here–we're talking about mathematical constructions. If you're using a straight edge, a compass, and a pencil, you're working with a construction.

Language:
English Language

Transcript

00:04

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

00:10

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

00:14

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

00:18

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

00:22

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

00:26

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

00:30

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

00:35

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

00:41

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

00:44

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

00:49

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

00:54

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

00:58

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

01:02

expensive using only these three tools we can

01:05

construct practically anything a perpendicular bisector a congruent angle

01:10

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

01:17

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

01:22

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

01:28

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

01:33

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

01:37

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

01:42

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

01:47

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

01:52

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

01:56

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

02:01

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

02:05

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

02:10

no Eiffel Tower but it'll do

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