Zoe is using the figure shown below to prove pythagorean theorem using triangle similarity: in the given triangle abc, angle a is 90o 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? by distribution, ac2 plus ab2 = bc multiplied by the quantity dc plus ab. by distribution, ac2 plus ab2 = bc multiplied by the quantity dc plus bd. by distribution, ac2 plus ad2 = bc multiplied by the quantity dc plus ab. by distribution, ac2 plus ad2 = bc multiplied by the quantity dc plus bd.

By distribution  AC^2+AB^2=BC(DC+BD)

Step-by-step explanation:

We can find the step by the below explanation,

Here, ABC is a right angles triangle in which

And,             (shown on figure)

Where,

Now, In triangles ABC and ABD,

 (right angle triangles)

( reflexive)

Thus, ,

Therefore,

⇒ ---------(1)

Similarly, we can prove,

⇒

⇒ -----(2)

On adding equation (1) and (2)

⇒

⇒           (because BC= BD+DC)

Which is the required Pythagorean Theorem.  

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.  

the answer will be b x² +x-1

step-by-step explanation: