Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
2. Measuring and Constructing Segments
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Exercise 25 Page 17

To find how the segment lengths compare, take the difference between them. To calculate how many times longer the abdomen is, divide them.

Abdomen Length: 2 14 inches
Thorax Length: 1 34 inches
The abdomen is 12 inches longer and 1 27 times longer.

Practice makes perfect

When we measure a segment length with a ruler, we should use the Ruler Postulate. We will have to begin by estimating the coordinates for the abdomen and thorax.

Abdomen

The first step is to align the first red line with a coordinate on the ruler. In the given diagram, this is 0.

The second coordinate is where the red line in the middle aligns with the ruler. The precision should be to the nearest 14 inch, so we estimate the coordinate to be at 2 14 inches.

Now we will use the Ruler Postulate to calculate the length of the abdomen. We should take the absolute value of the difference between the coordinates. |2 14 - 0|= 2 14 The length of the abdomen is, therefore, 2 14 inches.

Thorax

We can use the same procedure to find the length of the thorax. The thorax starts at the red line in the middle. We have already estimated the coordinate for the line when measuring the abdomen, 2 14 inches.

Now, we can measure the end point, which will be where the last red line aligns with the ruler. It seems to be at approximately 4 inches.

With these coordinates, we can calculate the length using the Ruler Postulate. We will take the absolute value of the difference between the points. |4-2 14|=1 34 The length of the thorax is 1 34 inches.

Difference and Ratio

To calculate how much longer the abdomen is than the thorax, we should take the difference between them. From previous calculations, we know that the abdomen is 2 14 inches and the thorax 1 34 inches.
2 14-1 34
â–Ľ
Simplify
9/4-7/4
2/4
1/2
The result is that the abdomen is 12 inches longer than the thorax. To calculate how many times longer the abdomen is, we should divide the lengths. This will tell us the ratio between the lengths.
2 14Ă· 1 34
â–Ľ
Simplify
9/4Ă·7/4
9/4*4/7
9*4/4*7
9/7
1 27
The abdomen is 1 27 times longer than the thorax.