if B is between A and C, D is between C and E, and C is the midpoint of both segments BD and Segment AE, then segment AB congrue

Question

3 years ago

10

nt segment DE

1 answer:

TiliK225 [7] · Answer 1 · 2022-09-21T02:07:18+03:00

The five statements and reasons below have proved that Segment AB is congruent to segment DE;

<u><em>Statement 5; AB ≅ DE</em></u>

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