Unit 6.3 Drawing Shapes with Given Conditions
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so he doesn’t have to make all these shapes himself.
Yeah, he’s got his own personal sweatshop going on here…
Tristan began the day by handing out one triangle each to his siblings, who are tasked with [Tristan hands one triangle to each brother]
creating similar versions of those triangles to add to the pile.
The second eldest brother, Tripp, got a triangle with side lengths of 27 inches, 36 inches and 45 inches.
Recognizing that all those measurements could be reduced…Tripp quickly realized he was
dealing with a 3, 4, 5 triangle.
So he drew one of those… and then, for good measure, multiplied all those measurements [Measurements of Tripp's triangle multipled by 2]
by 2 to get 6, 8, and 10…and drew a triangle with those side lengths as well.
Who knows…maybe the extra work would get him an additional five minutes for his daily [Tripp standing on a beach and Tristan orders him back to work]
break… The third oldest brother, Trigger, was given
a triangle with two of its three angles measuring 79 and 33 degrees.
He was just about to grab his protractor to measure the angle of the third side… [Trigger looking for a protractor]
…when he realized that, to draw a similar triangle, you only need measurements of two angles.
And…that’s exactly what he did.
Granted, it was a much smaller triangle than the one he was given, but the angles were
the same, and that’s all that matters.
Besides, it’s not like he’s getting paid by the inch. [Trigger in a room with a microscope]
The youngest brother, Triton, received a triangle with two side lengths labeled – 5 inches
and 12 inches – and the angle between those two sides labeled as 90 degrees.
It was, admittedly, a tad unfair that the youngest brother was given the toughest triangle, [Triton poking Tristan who is tied to a pole]
but Triton has never been one to stray from a challenge.
Eventually, he recalled the Side-Angle-Side rule…
…namely, that as long as the side lengths of two triangles are proportional, and the
angle between them is congruent, then the two triangles are similar.
So Triton tripled the measurement of the sides to create a triangle with sides of 15 inches and 36 inches… [Triton's triangle with measurements]
…the third side measured 39 inches, not that he even needed to know that…
…and preserved that same 90 degree angle between them.
Tristan is pretty pleased with his workers’ progress, but he’d better be careful.
His brothers have recently discovered what it means to “unionize”… [Tristan's brothers band together and look sternly at Tristan