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Is the diagonal of a square the same as its side?
Not always, the diagonal can be figured out using the Pythagorean Theorem (a²+b²=c²). Where the diagonal is the hypotenuse (c). By rearranging the Pythagorean Theorem, you can see that the diagonal of a square is always 1.4 times the side of the square.
Why is the pitchers mound not in the center of the baseball diamond?
This is because the rules of baseball say the mound is a distance from homeplate that is less than halfway the distance between homeplate and 2nd base. The distance is the same between each base in order (the same from home to 1st, 1st to 2nd, 2nd to 3rd, 3rd to home.) This results in the distance between homeplate and 2nd equal to the distance between 1st and 3rd. If you draw a line between homeplate and 2nd, and a line between 1st and 3rd, the lines will intersect in the center of the baseball diamond. However, the center point will be behind the pitcher's mound. You can use the Pythagorean Theorem to prove the distance from the mound to home is less than the center point, but that is another question. (Hint: The distance squared from home to first plus the distance squared from first to second divided by 2).
Why the distance formula is not needed to find the distance between two points that lie on a horizontal or vertical line?
It is used, except that, because one set of coordinates are the same, the formula collapses into a simpler form.
How do you place four points equidistant from each other?
To place four points equidistant from each other, you would need to arrange them in the shape of a perfect square. This means that each point would be the same distance away from the other three points, forming equal sides of the square. The distance between each point can be calculated using the Pythagorean theorem if the coordinates of the points are known.
What is the Converse of isosceles triangle theorem?
The isosceles triangle theorem states that if two sides of a triangle are congruent, the angles opposite of them are congruent. The converse of this theorem states that if two angles of a triangle are congruent, the sides that are opposite of them are congruent.
