which theorem explains why the circumcenter is equidistant from the vertices of a triangle

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which theorem explains why the circumcenter is equidistant from the vertices of a triangle 767
which theorem explains why the circumcenter is equidistant from the vertices of a triangle 767

The theorem that explains why the circumcenter is equidistant from the vertices of a triangle is called “AAS”. The AAS theorem states that if you connect any point on the circle to two points on the opposite side of an angle, then all three are equidistant.

This theorem is a special case of the general result that if we draw any line through two points on opposite sides of an angle, then it will be equidistant to all three.

Some other examples where this would be useful are in constructing rectangles and parallelograms. We can construct these shapes by drawing a diagonal that bisects one side from another and doing so for both pairs of opposing sides; as long as the diagonals cut perpendicularly into both corners they will form right angles with each other which means their lengths must match up perfectly. This gives us what’s called “corresponding parts” which tells you how much material you need at hand before beginning construction- no measurements required! If the corresponding parts match up with each other then you’ll know that, no matter the size of your shape, it will always be a rectangle or parallelogram.

In an isosceles triangle (triangle which has two congruent sides and two corresponding angles) we can find not just one but two different points on opposite sides of an angle from which to draw through all three vertices. The point where these lines intersect is called the circumcenter- a circle drawn around this point would have its circumference equidistant to all three points in question. This means that any line drawn through either vertex A or C will also go through B; any line drawn between VB or VC will also go through AC, so long as they’re parallel to this line.

Let’s say we have a triangle and the circumcenter is at point P, which is equidistant from A and C. If you connect B to that same intersection point it would create an angle of 180-90=90 degrees because both sides are congruent (the right angles). You can also take any side of your shape or figure: if parts match up with each other then you’ll know that no matter the size, it will always be a rectangle or parallelogram. The shortest distance to go through three points without crossing over itself is straight across in one direction only; this means pythagorean theorem won’t work here (it works on triangles where all three interior angles measure less than 90 degrees).

What is the theorem that explains why all three points from a triangle are equidistant to each other?

The parallel postulate can be formulated in many different ways. One of them is: “No two lines running through the same point will ever intersect.” This means no matter how close together you draw your two lines, they’ll never cross paths as long as they’re not going through one particular point which we know by definition isn’t possible for this case because our points A and C have an intersection at the circumcenter P. We also know it’s true because if you take any side of your shape or figure: if parts match up with each other then you’ll know that no matter the size, it will