Are the polygons similar? If they are, choose the correct similarity statement and scale factor. Not drawn to scale.

Option B:

Explanation:

The polygons are similar because in , the measure of ∠R=32°

Also, in , the measure of ∠U=32°

Now, we shall find the scale factor,

Since, , then the sides are proportional which is given by,

Substituting the values of RS and UV from the figure, we get,

Simplifying, we have,

Thus, the scale factor is

Hence, Option B is the correct answer.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it