Question

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.
B
A
D
C
Part A: Identify a pair of similar triangles. (2 points)
t B: Explain how you know the triangles from Part A are similar. (4 points)
A
Part C: If DB = 9 and DC = 4, find the length of segment DA. Show your work. (4 points)

Answer 1

1. The pair of similar triangles are ∆ABC and ∆ADB

2. The triangles are similar by AA postulate

3. The value of segment DA is 6

Similar triangles are triangles with equal corresponding angles and equal side ratios.

1. The pair of similar triangles in the figures are ∆ABC and ∆ADB.

2. angle BAC is equal to angle ADB and angle B is equal to angle B, therefore the triangles are similar by AA postulate.

3. To find DA we need to find DB

using similarity theorem;

let AB = x

13/x = x/9

x² = 13 × 9

x² = 117

Using Pythagorean theorem

AB)² = 9² + AD)²

117 = 81 + (AD)²

AD)² = 117 - 81

AD = √ 36

AD = 6

Therefore value of length DA is 6