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ABC is congruent with BAD. if AC=8m and AB = 17m, how long is AD?

For context. ABD and BAD are both upside-down right triangles that intersect and connect through points A and B

19m
20m
17m
15m

1 answer

Since triangles ABC and BAD are congruent, their corresponding sides must be equal in length.

Given:

  • AC = 8 m
  • AB = 17 m

In triangle BAD, since it is congruent to triangle ABC, we have:

  • AB = AB (common side, both triangles)
  • AC corresponds to AD in triangle BAD.

Since AB = 17 m, that value remains the same in both triangles.

Now, we know the relationship between the sides due to the congruence and the information we have. We need to find AD. In triangle ABC:

  • AC = 8 m
  • We are looking for the corresponding side AD.

Since the triangles are congruent:

  • AD (in triangle BAD) will also equal AC (in triangle ABC).

Thus, AD = AC = 8 m.

However, based on the options you provided (19m, 20m, 17m, 15m), it seems there may be an issue since none of the provided options correspond to our calculations. Please verify the context or give additional details about the triangles or any specific relationships they may have.