1. Find the ratio of the areas of two similar triangles if the ratio of similitude is:
a) 2:1
b) 1:9
C: 3:5
2. Find the ratio of two corresponding sides of two similar polygons if the ratio of
areas is:
a) 4:9
b) 16:25
c) 49:256
3. The lengths of the diameters of two circles are 6 and 10. Find the following
ratios:
a) the ratio of their radii
b) the ratio of their circumferences
c) the ratio of their areas

1. (a)4:1 (b)1:81 (c)9:25

2. (a)2:3 (b)4;5 (c)7:16

3. (a)3:5 (b)3:5 (c)9:25

Step-by-step explanation:

1. Given the ratio of similitude of two similar triangles, the ratio of their areas is the square of the ratio of similitude.

(a)2:1

Ratio of Area

(b)1:9

Ratio of Area

(c)3:5

Ratio of Area

2. Given the ratio of the areas of the sides of two similar polygons, the ratio of the sides is the ratio of the square root of their areas.

(a)4:9

Ratio of Sides

(b)16:25

Ratio of Sides

(c)49:256

Ratio of Sides

3.Lengths of the Diameter  are 6 and 10.

Diameter = Radius/2

Therefore, their radii are 3 and 5.

(a)Ratio of their Radii =3:5

(b)Since the circumference is still a length, Ratio of their Circumference =3:5

(c)Ratio of their Areas

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.