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Explain Bot To prove that BD is congruent to CE, we need to show that they have the same length.
Explanation:
In the given problem, we are given that C is the midpoint of BD, which means that C divides BD into two equal halves. We are also given that D is the midpoint of CE, which means that D divides CE into two equal halves.
We can start by drawing a diagram to visualize the situation:
B ____________ D
\ | /
\ | C /
\ | /
\ | /
\ | /
\|/
C
|
|
E
In order to prove that BD is congruent to CE, we can use the midpoint theorem. The midpoint theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of its length.
Therefore, we can use the midpoint theorem to state that BC is parallel to DE and that BD is congruent to CE.
Now, to prove that BD is congruent to CE, we can use the following steps:
1. Statement: C is the midpoint of BD.
Reason: Given.
2. Statement: D is the midpoint of CE.
Reason: Given.
3. Statement: BC is parallel to DE.
Reason: Midpoint theorem.
4. Statement: Triangle BCD is congruent to triangle CDE.
Reason: Each side of triangle BCD is congruent to the corresponding side of triangle CDE.
5. Statement: BD is congruent to CE.
Reason: Corresponding parts of congruent triangles are congruent (CPCTC).
Therefore, based on the midpoint theorem and congruence of triangles, we can conclude that BD is congruent to CE.