Respuesta :
The five statements and reasons below have proved that Segment AB is congruent to segment DE;
Statement 5; AB ≅ DE
We are Given:
B is between A and C
D is between C and E
C is the midpoint of both segments BD and AE
AB ≅ DE
We want to prove that;
AB ≅ DE
Statement 1; C is the midpoint of BD and AE.
Thus; BC = CD and AC = CE
Reason; because a midpoint divides a segment into 2 equal parts.
Statement 2; AB + BC = AC and CD + DE = CE
Since B is between A and C and D is between C and E, then we can say;
AB + BC = AC
CD + DE = CE
Reason; property of line segment addition
Statement 3; AB + BC = CD + DE
Since AC = CE, then using substitution property of equality on statement 2, we have; AB + BC = CD + DE
Reason; Substitution property of Equality
Statement 4; AB + BC = BC + DE
Since BC = CD, the using substitution property of equality on CD in statement 3, we have; AB + BC = BC + DE.
Reason; Substitution property of Equality
Statement 5; AB ≅ DE
Using subtraction property of equality on statement 4, BC will cancel out to give; AB = DE
Equal segments are congruent and so we can write; AB ≅ DE
Reason; Subtraction property of equality
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