Question

3 which of the following are impossible? give a reason for your answer.
a. (overline{ab} cong overline{db})
b. line ab bisecting segment cd
c. (overline{fg}) bisecting (overline{db})
d. a pentagon created by 5 rays

1. if (ad = 15), (be = 7), (cb = 3db), and (overline{ac} cong overline{db}), find (de).

diagram: a line with points a, c, d, b, e in sequence

Explanation:

Step1: Define variables for segments

Let \( DB = x \), then \( CB = 3x \).

Step2: Express AC and AD in terms of x

\( AC = AD - CD \), but from the line, \( AD = AC + CD \). Since \( AC = DB = x \), \( AD = x + CD = 15 \), so \( CD = 15 - x \). Also, \( CB = CD + DB \Rightarrow 3x = (15 - x) + x \Rightarrow 3x = 15 \).

Step3: Solve for x

\( 3x = 15 \Rightarrow x = 5 \), so \( DB = 5 \).

Step4: Calculate DE

\( DE = DB + BE = 5 + 7 = 12 \).

Answer:

12