Similar Shapes help?

Question

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there are two questions. Thank you for any help.​

 

Answer 1

(1a)

Segment is parallel to Segment .

and by the property of transversal.

From AA property of similar triangles, .

Therefore, .

(1b)

Length of sides are  , and .

Side-Splitting theorem : if Segment Segment , then .

Therefore

Answer 2

(2)

The height of larger pyramid is 12 m.

The height of smaller pyramid is 6 m.

The volume of larger pyramid is 400 m³.

(a)

Find the scale factor of the smaller pyramid to the larger pyramid.

In two similar geometric figures, the ratio of their corresponding sides is called the scale factor.

Scale factor of the smaller pyramid to the larger pyramid

Answer 3

(2b)

Find the ratios of the areas of the bases of the smaller pyramid to the larger pyramid.

Area of the base of square pyramid, where s is the side length of base.

Height of the pyramid is .

Ratios of the areas of the bases of the smaller pyramid to the larger pyramid

Answer 4

(2c)

Find the volume of the smaller pyramid to the larger pyramid.

Volume of square pyramid, where s is the side length of base and h is the height of pyramid.

Height of the pyramid is .

Ratios of the volume of the smaller pyramid to the larger pyramid

Answer 5

(2d)

The volume of larger pyramid is 400 m³.

From part (2c):

Ratios of the volume of the smaller pyramid to the larger pyramid

Volume of the smaller pyramid is