(05.01 lc) 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. the figure shows triangle abc with right angle at a and segment ad. point d is on side bc. which of these could be a step to prove that bc2 = ab2 + ac2? (6 points) group of answer choices by the cross product property, ab2 = bc multiplied by bd. by the cross product property, ac2 = bc multiplied by bd. by the cross product property, ac2 = bc multiplied by ad. by the cross product property, ab2 = bc multiplied by ad.

The Full Proof is given below.

The choice for the proof is

By the cross product property we have

Step-by-step explanation:

Given:

In triangle ABC, angle A is 90° and

segment AD is perpendicular to segment BC.

To Prove:

Proof:

In  Δ ABC and Δ DBA

∠A ≅ ∠D    …………..{ measure of each angle is 90° given }

∠B ≅ ∠B    ………{Reflexive Property}      

Δ ABC ~ Δ DBA ….{Angle-Angle Similarity test}

If two triangles are similar then their sides are in proportion.

By the cross product property we have

( 1 )

Similarly ,

In  Δ ABC and Δ DAC

∠A ≅ ∠D    …………..{ measure of each angle is 90° given }

∠C ≅ ∠C    ………{Reflexive Property}      

Δ ABC ~ Δ DAC ….{Angle-Angle Similarity test}

If two triangles are similar then their sides are in proportion.

By the cross product property we have

( 2 )

Now by Adding 1 and 2 we get

Therefore,

..which is Pythagoras Theorem ...Proved