Why midpoint of hypotenuse is equidistant from vertices?
Why midpoint of hypotenuse is equidistant from vertices?
Since the triangle is right it’s orthocentre lies on the midpoint of hypotenuse. With o orthocentre as centre and radius as distance between o and one of the vertices a circle passes through the vertices. The distances are length of radii. Hence they are equidistant.
How is the midpoint of the hypotenuse related to the three vertices of the right triangle?
In a right triangle, the midpoint of the hypotenuse is equidistant from all three vertices.
What is special about the midpoint of a hypotenuse?
The midpoint of the hypotenuse of a right triangle is the circumcenter of the triangle. Let A(a,0), B(b,0) and C(b,c) be any three points on the given circle. Thus, the midpoint of the hypotenuse is equal to the center of the circle.
What point is equidistant from the sides of a triangle?
incenter
The incenter is equidistant from the sides of the triangle. That is, PI=QI=RI . The circle drawn with the incenter as the center and the radius equal to this distance touches all three sides and is called incircle or the inscribed circle of the triangle.
Is circumcenter midpoint of hypotenuse?
The circumcenter of a right triangle is the midpoint of the hypotenuse.
Is the circumcenter of a right triangle always the midpoint of the hypotenuse?
The circumcenter of a right triangle lies exactly at the midpoint of the hypotenuse (longest side). The circumcenter of a obtuse triangle is always outside of the triangle. The INCENTER(I) of a triangle is the point on the interior of the triangle that is equidistant from the three sides.
How do you find the midpoint of a right triangle?
QD is the median drawn to hypotenuse PR. To prove: QS = 12PR….Midpoint Theorem on Right-angled Triangle.
| Statement | Reason |
|---|---|
| 4. TS ⊥ PQ. | 4. TS ∥ QR and QR ⊥ PQ |
How do u find the midpoint of a triangle?
How do I find the midpoint of a triangle?
- Find the midpoint of the sides of the triangle.
- Measure the distance between the two end points, and divide the result by 2.
- Alternatively, add the two x coordinates of the endpoints and divide by 2.
- Draw a line between a midpoint and its opposite corner.
