Fill the missing boxes and how do you know? Triangle Mid segment Theorem

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Step-by-step explanation:

The differences of coordinates are ...

  E-D = (-2, 0) -(-4, -2) = (-2+4, 0+2) = (2, 2)

The slope is the ratio of the y-difference to the x-difference:

  slope of DE = ∆y/∆x = 2/2 = 1

The length is the root of the sum of the squares of those differences:

  length of DE = √(2² +2²) = √8 = 2√2

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Similarly, the slope of CB is found from ...

  B -C = (1, -2) -(-3, -6) = (1+3, -2+6) = (4, 4)

  slope = 4/4 = 1

And the length is ...

  length of CB = √(4² +4²) = 4√2

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Because the slopes of DE and CB are both 1, DE ║ CB.

DE = 2√2 and CB = 4√2.

Because 2√2 = (1/2)·4√2, DE = 1/2·CB.

each side has a different length.  

step-by-step explanation: