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A triangle marked clockwise from the left vertex as upper A upper B upper C. Congruent line segments and angles are marked.

In the figure, ΔDBE has the following side lengths: DB¯¯¯¯¯¯¯¯=12 units, BE¯¯¯¯¯¯¯¯=7 units, and DE¯¯¯¯¯¯¯¯=14 units. What is the length of AB¯¯¯¯¯¯¯¯ ?

(1 point)
Responses

24 units
24 units

14 units
14 units

12 units
12 units

28 units
28 units
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1 answer

To determine the length of \( AB \), we can analyze triangle \( DBE \) given the side lengths:

  • \( DB = 12 \) units
  • \( BE = 7 \) units
  • \( DE = 14 \) units

Next, we can check if triangle \( DBE \) is congruent to triangle \( ABC \). If \( \triangle DBA \) is congruent to \( \triangle DBE \), then the corresponding sides will also have equal lengths, meaning \( AB \) would be equal to \( DE \).

Since given \( DE = 14 \) units in triangle \( DBE \), we can say:

\[ AB = DE = 14 , \text{units} \]

Therefore, the length of \( AB \) is:

14 units