The missing information in the proof is DE=a
What is the distance formula?
The distance between two points of coordinate (x₁,y₁) and (x₂,y₂) is given by the formula
d=√(x₂-x₁)²+(y₂-y₁)²
Given that,
D is mid-point of AB.
E is mid-point of AC.
We have to find the missing information in the given proof of DE=(1/2)BC.
D and E are the mid-point of AB and AC respectively.
From the picture given below it is clear that
The coordinates of point A are (2b,2c)
The coordinates of point B are (0,0)
The coordinates of point C are (2a,0)
The coordinates of point D are (b,c)
The coordinates of point E are (a+b,c)
the distance formula is given by d=√(x₂-x₁)²+(y₂-y₁)²
Length of BC will be= √(2a-0)²+(0-0)² = 2a units
Length of DE= √(a+b-b)²+(c-c)²= a unit
DE=a unit
from above it is clear that, BC=2a=2DE
DE=(1/2)BC
Therefore The missing information in the proof is DE=a.
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