Which statement is necessarily true if BD is an attitude to the hypotenuse of right ABC?

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therealchaser21 therealchaser21 · Answer 1 · 2017-06-06T20:41:38+02:00

The first option. ADB is congruent to BDC because they if angle/angle. At least two angles are the same making it congruent.

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JeanaShupp JeanaShupp · Answer 2 · 2019-06-10T10:09:09+02:00

Answer: [tex]\dfrac{AB}{BC}=\dfrac{AC}{BD}[/tex]

Step-by-step explanation:

Given: Δ ABC is a right triangle right angled at B.

If BD is an attitude to the hypotenuse of right triangle ABC.

Then Δ ABD is a right triangle.

Now, in Δ ABC and Δ ADB

∠A=∠A [Reflexive property]

∠ABC=∠BDA [each 90°]

Then by AA similarity criteria,

Δ ABC ≈ Δ ADB

We know that in similar triangles, the corresponding sides are proportional.

Since side AB of Δ ABD is corresponding to side AC of Δ ABC.

and side BC of Δ ABD is corresponding to side BD of Δ ABC.

∴ we have,

[tex]\dfrac{AB}{AC}=\dfrac{BC}{BD}[/tex]

[tex]\Rightarrow\dfrac{AB}{BC}=\dfrac{AC}{BD}[/tex]