Question

Are the triangles similar? If so, what is the scale factor of ΔRPQ to ΔVAQ?

Answer 1

Answer:

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

                                         ⇒ $\frac{RP}{AV} = \frac{PQ}{AQ}$

                                         ⇒$\frac{6}{3} = \frac{8}{4}$

                                         ⇒ 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.      

Answer 2

Yes 2:1 you know this because the short sides, 3 and 6 are in the same ratio as the long sides, 4 and 8