Question

In triangle ABC, B is 90°, E is the mid point of AC. Prove that BE is equal to half AC.
​

Answer 1

Using the Pythagorean Theorem:

The original right △△ ABC

(AC)2=(AB)2+(BC)2(AC)2=(AB)2+(BC)2

Right △△ ADB

(AB)2=(AD)2+(BD)2(AB)2=(AD)2+(BD)2

Right △△ BDC

(BC)2=(DC)2+(BD)2(BC)2=(DC)2+(BD)2

Using substitution:

(AC)2=[(AD)2+(BD)2]+[(DC)2+(BD)2](AC)2=[(AD)2+(BD)2]+[(DC)2+(BD)2]

Dropping the square brackets ([ ]) and combining like terms