Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity. In the given triangle ABC, angle A is 90°, and segment AD is perpendicular to segment BC.

Part A: Identify a pair of similar triangles. (2 points)

Part B: Explain how you know the triangles from Part A are similar. (4 points)

Part C: If DB = 9 and DC = 4, find the length of segment DA. Show your work. (4 points)

please help

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  A)  ΔDBA ~ ΔABC

  B) AA similarity: angle B is shared, and both triangles are right triangles

  C) DA = 6

Step-by-step explanation:

A) In this geometry similarity can be shown by matching/comparing angles. Right triangles are AA similar if one of the acute angles is the same in each triangle, because the right angle is already the same in each.

Angle B is part of both triangle ABC and triangle DBA. We have chosen those names to have the right angle vertex named first, followed by the shared angle vertex. This ensures that the similarity statement properly identifies corresponding vertices.

  ΔABC ~ ΔDBA

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B) The similarity logic is discussed in part A.

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C) Another set of similar triangles is ...

  ΔCDA ~ ΔADB

Then we can write the proportion for corresponding sides as ...

  DA/DC = DB/DA

  DA² = DC·DB . . . . . . cross multiply

  DA = √(DC·DB) = √(4·9) = √36 . . . . . square root and substitute numbers

  DA = 6

x + 4/7

step-by-step explanation:

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