Home
Class 11
PHYSICS
Prove that the mid-point of the hypoten...

Prove that the mid-point of the hypotenuse of right angled triangle is equidistant from its vertices.

Text Solution

AI Generated Solution

To prove that the midpoint of the hypotenuse of a right-angled triangle is equidistant from its vertices, we can follow these steps: ### Step 1: Define the Triangle and Midpoint Let triangle ABC be a right-angled triangle with the right angle at vertex A. Let D be the midpoint of the hypotenuse BC. ### Step 2: Use Coordinate Geometry Assign coordinates to the points: - Let A be at (0, 0) ...
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    DC PANDEY ENGLISH|Exercise Exercise|13 Videos
  • CALORIMETRY & HEAT TRANSFER

    DC PANDEY ENGLISH|Exercise Level 2 Subjective|14 Videos

Similar Questions

Explore conceptually related problems

Prove that the mid-point of the hypotenuse of a right triangle is equidistant from its vertices.

In Fig. 14.40, a right triangle B O A is given. C is the mid-point of the hypotenuse A B . Show that it is equidistant from the vertices O ,\ A and B . (FIGURE)

Find a point on the base of a scalene triangle equidistant from its sides.

Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle

Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.

If D is the mid-point of the hypotenuse A C of a right triangle A B C , prove that B D=1/2A C

If the equation of the hypotenuse of a right - angled isosceles triangle is 3x+4y=4 and its opposite vertex is (2, 2), then the equations of the perpendicular and the base are respectively

Prove by vector method, that in a right-angled triangle ABC, AB^(2) + AC^(2) = BC^(2) , the angle A being right angled. Also prove that mid-point of the hypotenuse is equidistant from vertex.

[ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle.Explain why O is equidistant from A ,B and C .(The dotted lines are drawn additionally to help you).]

A point on the hypotenuse of a right triangle is at distances a and b from the sides of the triangle. Show that the minimum length of the hypotenuse is (a^(2/3)+b^(2/3))^(3/2)