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Please help !!
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 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 i class=

Respuesta :

varshamittal029

ΔABD and ΔACD are similar (By A-A-A) and The length of DA is 6.

The triangles where all the corresponding sides of the two triangles are in equal proportion are called similar triangles.

In triangle ΔABC ∠BAC=90°

Let ∠ABC=x

then ∠ACB=90°-x

In triangle  ΔADC, ∠ADC =90°

∠ACB=∠ACD=90°-x

∠DAC= 180°-(∠ADC+∠ACD)= 180°-(90°+90°-x)= x

In triangle  ΔADB , ∠ADB =90°

∠ABD=x

∠BAD=90°-x

Between triangles ΔABD and ΔACD

∠ABD=∠DAC (=X)

∠BAD∠ACD (=90°-x)

∠ADB=∠ADC (=90°)

from the above, it is clear that triangles ΔABD nad ΔACD is similar. (By A-A-A)

So sides are in equal proportion in 2 triangles,

AD/DC= BD/AD

⇒AD²= BD*DC

⇒AD²=9*4

⇒AD²=36

⇒AD=6

⇒DA=6

Therefore triangles ΔABD and ΔACD are similar (By A-A-A) and The length of DA is 6.

Learn more about similar triangle

here: https://brainly.com/question/14285697

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