SOLUTION: a ∥ b ∥ c and B is the midpoint of AC. AB = 2x + 5, BC = x + 7, and DE = 3x + 6. x = Find the length of DE. DE = Because a ∥ b ∥ c and B is the midpoint of AC,E is t

Question 1193343: a ∥ b ∥ c and B is the midpoint of AC.
AB = 2x + 5, BC = x + 7, and DE = 3x + 6.
x =
Find the length of
DE.
DE =
Because a ∥ b ∥ c and B is the midpoint of
AC,E is the midpoint of
DF and EF =
.
Find the length of
EF.
Answer by proyaop(69) (Show Source): You can put this solution on YOUR website!
Certainly, let's break down the problem step by step.
**1. Find the value of x:**
* Since B is the midpoint of AC, AB = BC.
* Therefore, 2x + 5 = x + 7
* Solving for x, we get: x = 2
**2. Find the length of DE:**
* DE = 3x + 6
* Substitute the value of x: DE = 3(2) + 6
* DE = 12
**3. Determine EF:**
* Given: a ∥ b ∥ c (lines a, b, and c are parallel)
* Since B is the midpoint of AC and lines are parallel, E must be the midpoint of DF.
* This is a property of parallel lines: Lines intersecting parallel lines create proportional segments.
* If E is the midpoint of DF, then EF = DE
* **Therefore, EF = 12**
**Summary:**
* x = 2
* DE = 12
* EF = 12
Let me know if you have any other questions or problems to solve!

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