Question

Question 9 (Essay Worth 10 points) (03.06 HC) 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)

Answer 1

In the case above, the length of Angle DA is 6 and angle ABD ≈ Angle CAD.

What is the angle about?

Note that:

Δ ABC , A = 90

To find length of DA :

Let Δ ACB = x

So Δ ABC = 90 -x

For Δ ABC and ADC:

Δ ADB = Δ ADC  (90°)

Δ ABD = Δ DAC (90 - x)

For Δ ABC ≈  ADC:

$\frac{AD}{DC} = \frac{BD}{AD}$

AD² = BD. CD.

AD²= 9 . 4

AD²= 36

AD = 6

Therefore, In the case above, the length of Angle DA is 6 and angle ABD ≈ Angle CAD.

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