Are the triangles similar? if so, what is the scale factor of δrpq to δvaq? a)nob)yes; 2: 1c)yes; 2: 3d)yes; 3: 4

Option B) YES; 2:1

Step-by-step explanation:

In these triangles ΔRPQ and ΔVAQ we have been given few measurements like

∠RPQ = ∠VAQ = 90°

Length of AV =3, AQ = 4 &

Length of RP =6, PQ = 8

Now we have been asked about the scale factor of these two triangle and similarity between them.

As we know if two sides of a triangle is in the same ratio of the other triangle and angle between these sides is same then triangles are similar.

In other words ratio of sides RP:AV = PQ:AQ

                                         ⇒

                                         ⇒

                                         ⇒ 2:1 =2:1

And angle between them ∠RPQ = ∠VAQ = 90°

Therefore bothe the triangles are following rule of SAS so similar with a scale factor of 2:1.