if T is the midpoint of segment CE then CT=TE the instructions say name the definition, postulate or theorom and im confused

1 answer:

6 0

This is the definition of the midpoint of a line segment.

The midpoint is, by definition, the point on the line segment that splits it in two equal (congruent) segments.

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The surface area of a cone is 54 square inches. What is the surface area of a similar cone that is three times as large?

12345 [234]

<u>Given</u>:

Given that the surface area of the cone is 54 square inches.

We need to determine the surface area of the cone that is similar to the cone three times large.

<u>Surface area of the similar cone:</u>

Let us determine the surface area of the similar cone.

The surface area of the similar cone can be determined by multiplying the surface area of the cone by 3. Because it is given that the similar cone is three times large.

Thus, we have;

$SA = 3 \times 54$

$SA=162$

Thus, the surface area of the similar cone is 162 square inches.

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What is the sum of the squares of the lengths of the $\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12

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A picture can help.

The median to the long side divides the isosceles triangle into two right triangles with hypotenuse 10 and short leg 6. Thus the long leg (median of interest) is found by the Pythagorean theorem to be

... √(10² -6²) = √64 = 8

Then the midpoint of the short side is found to be 6 + (6/2) = 9 units to the side and 8/2 = 4 units above the opposite vertex. Hence the square of the length of that median is 9² + 4² = 97.

The sum of squares of interest is

... 8² + 2×97 = 258