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9.21. Find the side of an equilateral triangle whose area equals (a) The sum of the areas of two equilateral triangles whose sides have lengths 9 and 12 (b) The difference of the areas of two equilateral triangles whose sides have lengths 17 and 15 (c) The area of a trapezoid whose bases have lengths 6 and 2 and whose altitude has length 9 23 (d) Twice the area of a right triangle having a hypotenuse of length 5 and an acute angle of measure 30

(9.6)

Note!



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9.22. Find the area of trapezoid ABCD in Fig. 9-21, if: (a) b (b) m (c) AB (d) AB (e) AB 25, b 15, and h 6.9 30 , b 45 , b 24, and b 13, and b b 20 6 7 7

(9.7)

Euclid s Elements began with only five postulates. We shall go through them with an eye for alternatives.

POSTULATE 1:

One and only one straight line can be drawn through any two points. ( 2, Postulate 11)

We further postulate that there exist at least two points, A and B, so there exists a straight line.





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4.1 What are the three basic types of style that create the cascade in CSS 4.2 What is their order of precedence 4.3 What are two components of a declaration 4.4 Name three subcomponents and provide a brief description of the components that make up XSL. 4.5 Which of these is not one of the eight border styles dotted dashed solid single double groove ridge inset outset 4.6 What is the default value for background a. white b. transparent c. inherited d. black 4.7 Which one of these PI examples is correct a. <!-- xml-stylesheet type="text/css" href="my_css.css" --> b. < xml-stylesheet type="text/css" href="my_CSS.css" > c. < xml-stylesheet style="text/css" href="my_CSS.css" > d. < xml-stylesheet style="text/css" href="my_CSS.css" /> 4.8 What was added for use with fonts to the CSS speci cation in CSS2 4.9 Give an example of one of the answers from Question 4.8, and explain its use and syntax. 4.10 What are three properties of the border style

POSTULATE 2:

Most businesses operate using the accrual method of accounting. Under the accrual basis of account ing, revenue is recognized only when it is earned and expense is recognized only when it is incurred.

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A line segment can be extended in either direction indefinitely. ( 1, description of a line)

Traditionally, we suppose that the line through A and B looks like Fig. 19-1(a), but our postulates do not rule out the possibility of Fig. 19-1(b). In Fig. 19-1(b), the line reaches no end in either direction, and thus in some sense can be extended indefinitely. Remember that the original meaning of geometry comes from earth and measure. The straightest line that could be drawn on the earth would wrap around to form a great circle, as discussed in 17.

Fig. 19-1

A circle can be drawn with any center and radius. ( 2, Postulate 14)

POSTULATE 3:

When we believe this postulate, we believe that we have a plane with no end in any direction on which we could find circles with ever-larger radii. It could be that this leads to circles like ripples on the surface of a still pond, as shown in Fig. 19-2(a). However, if our plane were more like the surface of the Earth, our circles might look more like the circles of latitude, shown in Fig. 19-2(b).

Summary

Fig. 19-2

POSTULATE 4:

This postulate enables us to measure angles in degrees. A plane would have to be somehow lumpy or uneven if some right angles could be bigger than others.

POSTULATE 5:

Through a given point not on a given line, one and only one line can be drawn parallel to a given line. ( 4, Parallel-Line Postulate)

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