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)

Question

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Respuesta :

varshamittal029 varshamittal029 · Answer 1 · 2022-06-29T07:46:11+02:00

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.

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