Question

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

Answer 1

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

Answer 2

Answer:
`(AB)/(BC)=(AC)/(BD)`

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,

`(AB)/(AC)=(BC)/(BD)`

`\Rightarrow(AB)/(BC)=(AC)/(BD)`