Question

Are the polygons similar? If they are, write a similarity statement and give the scale factor.

Answer 1

The polygons are similar

ΔRST ≈ ΔUVW;
`(5)/(6)`

Explanation:

Data:

The triangles have similar angles at U and R.

Therefore, the triangles must have the similar first letter naming.

Starting the triangle at U, the triangle will be named: UVW.

The second triangle will be named starting at R: RST

The ratio of the areas is the ratio of the corresponding sides. Therefore, taking the ratio of the bases:

RST : UVW will be :
`(15)/(18) = (5)/(6)`

Answer 2

Yes. The two triangles are similar in that.

ΔRST ≡ ΔUVW.

The scale factor of the similarity is,

Scale factor = RS/UV
= 10/12
=5/6