Prove that the midpoint of the hypotenuse of the right angle triangle is equal distance from its vertices
Answers
Given: right angle triangle
To Find : Prove that the midpoint of the hypotenuse of the right angle triangle is equal distance from its vertices
Solution:
Let say ΔABC is right angle at B
D is mid point of Hypotenuse AC
AD = DC = AC/2
Draw a line DE || AB
if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio
=> AD/DC = BE/CE
AD = DC
Hence BE = CE
DE || AB hence ∠CED =∠BED =90°
Comparing Δ BED & Δ CED
BE = CE
∠BED =∠CED=90°
DE = DE ( common)
hence Δ BED ≅ Δ CED
=> BD = DC
Hence AD = DC = BD
midpoint of the hypotenuse of the right angle triangle is equal distance from its vertices
QED
Hence proved
Learn More:
prove that if the hypotenuse of a right triangle is h and the radius of ...
https://brainly.in/question/13221257
The figure below shows two triangles EFG and KLM: Two triangles ...
https://brainly.in/question/9801492