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.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side 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)

Part A: Triangle BAD is congruent to BDA, triangle BAD is congruent to ADC, and triangle BDA is congruent to ADC.

Part B: With the AA similarity postulate which is used when you use the Pythagorean theorem, you can see that Segment AD makes 2 more right triangles that are similar to the whole triangle itself. D shares angle C with triangle BAC (the whole triangle) which then has a right angle at A.

Part C:  DB/AD = AD/DC, 9/x=x/4, 9x4=x times x, 9x4=36^2, 36 to the square root is 6, so 6=DA.

Explanation:

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