Question

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Answer 1

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: brainly.com/question/14285697

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