Right triangles have an interesting property, which is that you can easily cut them up to make two smaller versions of themselves. Start with a right triangle and draw an altitude. It turns out that the three triangles are similar,…
While finding the area of a triangle, we saw that a right triangle is half a rectangle. This lets us find the interior angles of a right triangle, too. The rectangle has four right angles. These are split up between…
It’s very simple to find the area of a right triangle. The right triangle is just half a rectangle. To show the two triangles that make up the rectangle are congruent, note that because segments perpendicular to the same segment…
After discovering that the perpendicular bisectors of the sides of a triangle meet at the circumcenter, it’s natural to wonder about the angle bisectors of the sides of a triangle. Drawing a picture, it appears that the angle bisectors meet…
After you construct an equilateral triangle, it’s natural to construct a perpendicular bisector. A perpendicular bisector of a segment is a line that intersects the segment at a right angle and cuts it into two equal parts. Start with this…
One of the simplest constructions in Euclidean geometry is the construction of an equilateral triangle – a triangle with all sides the same length. Start with a segment . Draw the circle with center going through and the circle with…
Today, I was playing around with a triangle: I drew two perpendicular bisectors, and wondered whether the third would intersect them. It certainly appears to! But what if the triangle is proportioned differently? It seems the three perpendicular bisectors will…
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