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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

8. Congruent and Similar Solids

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Exercise 8 Page 867

Congruent solids have the same shape and all of their corresponding dimensions are the same.

Similar, Congruent, or Neither? Congruent.

Practice makes perfect

Similar solids have the same shape and all of their corresponding dimensions are proportional. The ratio of corresponding linear dimensions is the scale factor. With this in mind, we will consider the given cylinders to determine whether they are similar or not.

We can see that the cylinder on the left has no length for the inner diagonal. Let's use the Pythagorean Theorem to find the inner diagonal length for the cylinder on the left, taking its height and the diameter of the base as the legs of the triangle.

c^2 = 15^2 + 8^2

▼

Solve for c

Calculate power

c^2 = 225 + 64

Add terms

c^2 = 289

sqrt(LHS)=sqrt(RHS)

c = 17

Since the diagonal of both cylinders has the same length, and both cylinders have the same diameter of the base, the length of the heights must also be the same. Therefore, both cylinders are congruent.

Subchapter links

Exercises p.867-870