Which polygons can be mapped onto each other by similarity transformations?

Solution:

Two polygons are said to be similar if ratio of their corresponding sides are same and their interior angles are congruent.

Consider Polygon 1 and Polygon 4

AB= DE= 8 units, AE= 6 units,

PT=QR= 4 Units, PQ= 3 Units

So, Polygon 1 ≅ Polygon 4

Now, Consider Polygon 2 and Polygon 3

LM=KO=6 units, LK=4 units

GF= 4 units, GH=FJ =4 Units

As you can see that polygon 2 and polygon 4 doesn't have corresponding proportional sides i.e .

So, Polygon 2  is not congruent to Polygon 4.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.