## SarahGardan

### Vector Art Illustrator     # A Property Of The Midpoint Of The Hypotenuse In A Right Triangle

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Prove that in a right angled triangle the mid point of the hypotenuse is equidistant from its vertices. I have asked similar question but with no satisfactory result.The midpoint of the hypotenuse BC is ( ). We can find the distance from each point to the midpoint and show that they are all equal. A better way to prove this is to cirgraphicscribe a circle around ABC. Since BAC is a right angle the hypotenuse BC is a diameter of the circle. We can draw the midpoint D and show that DA DB DC are all radii of the circle hence they are equal.Prove that in a right angled triangle the mid point of the hypotenuse is equidistant from its vertices. I have asked similar question but with no satisfactory result. So I solved it by myself. Bu

30.12.2008 Best Answer Let ABC be the right triangle right angled at B and AC is the hypotenuse and D is the midpoint of hypotenuse such that AD CD angle(ABC) 90degees Imagine triangle ABC is inscribed in a circle or semicircle such that AC is the diameter and so angle(ABC) is angle in a semicircle which is Status OffenAntworten 507.07.2007 This makes triangle ABC a 45-45-90 right triangle. angle DBC is 45 and then triangle DBC is also a 45-45-90 right triangle. Thus since angle DBC is 45 and angle C is 45 then DB DC opposite sides of congruent angles are congruent. Thus DB DC DA midpoint is equidistant from each vertex transitive propertyStatus OffenAntworten 5All right triangles inscribed in a circle have their vertices on the circle and the hypotenuse as the circles diameter. Thus the midpoint of the hypotenuse is the center of the circle nd all

Median drawn to the hypotenuse of a right triangle Theorem 1 In a right triangle the median drawn to the hypotenuse has the measure half the hypotenuse.