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In this problem, we will be exploring squares and their diagonals.
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Background information that is helpful is to be mindful that a square is made up of 490 -degree angles.
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The sum of the interior angles of any triangle is 180 degrees.
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To prove that the diagonals in a square are perpendicular to each other, we can look at the original vertex.
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We know that the vertex or the vertices in a square, are all 90 degrees.
00:34
So looking at this particular vertex, when it's split in half or when it's bisected by one of the diagonals, then it breaks down into two 45 degree angles.
00:48
So if we take a look, when we draw the two diagonals in a square, it creates 45, 45, 90 triangles.
00:59
So we have a 45 degree angle here.
01:03
Another 45 degree angle here.
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And then in order for the total sum of the interior angles of this triangle to equal 180 degrees, this angle would have to be equal to 90 degrees.
01:18
Anytime two lines intersect at a 90 degree angle, they are considered perpendicular.
01:25
And so given the formation of 445 -4590 triangles, we can conclude that the diagonals in a square are perpendicular.
01:35
So we attribute that to the formation of those 45, 45, 90 triangles...