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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

14 units
14 units

12 units
12 units

28 units
28 units

24 units
24 units
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1 answer

To find the length of \( AB \), we need to analyze triangle \( DBE \) and use the properties of congruent triangles.

In triangle \( DBE \):

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

First, we can apply the triangle inequality to see if triangle \( DBE \) is valid:

  1. \( DB + BE = 12 + 7 = 19 > DE \) (14) - Valid
  2. \( DB + DE = 12 + 14 = 26 > BE \) (7) - Valid
  3. \( BE + DE = 7 + 14 = 21 > DB \) (12) - Valid

Since triangle \( DBE \) is valid, we can also assume that triangle \( ABC \) might be congruent to triangle \( DBE \) based on congruent segments and angles.

If angles opposite to the sides are congruent in both triangles (a common assumption in congruent triangles), then:

  • If \( DE \) corresponds to \( AB \),
  • And \( DE = 14 \) units,

Thus, from congruence, we can conclude that: \[ AB = DE = 14 \text{ units.} \]

Therefore, the answer is \( 14 \) units.