Table of Contents
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 is mid point theorem Class 9?
The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
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 |
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.
Why is median half the hypotenuse?
The median of a triangle is a line drawn from one of the vertices to the mid-point of the opposite side. In the case of a right triangle, the median to the hypotenuse has the property that its length is equal to half the length of the hypotenuse.
Is the midpoint of the hypotenuse equidistant from its vertices?
Prove that the mid-point of the hypotenuse of a right angled triangle is equidistant from its vertices. Let AOB be a right angle triangle, with hypotenuse AB. We take OB along x-axis and OA along y-axis.
What is the hypotenuse of a right angled triangle?
Therefore the diagonals are hypotenuses of right angle triangles and their center is equidistant (the circle’s radius) from the vertices of the triangles. In a right angled triangle, the sides containing right angle are 8cm and 6cm. What is the height of this triangle corresponding to its hypotenuse?
Why is the centroid of a triangle equidistant from all vertices?
Since the CC is the only geometric centre which is equidistant from the three vertices of a triangle, hence the mid point of the hypotenuse has to be equidistant from all vertices. What is the centroid of paper cutouts of right-angled triangles and obtuse -angled triangles?
Which vertices of a right angled triangle lie on the circumference?
So, if we assume the hypotenuse of any right angled triangle as diameter of a circle with the mid point of the hypotenuse as centre of that circle, the vertex of that triangle will definitely lie on the circumference,as it is a right angle. So, all three vertices of the given triangle lie on the circumference.