SS - Angle Side Side What about SSA (Side Side Angle) theorem? There is NO SUCH THING!!!! The ASS Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non included angle, then triangles are NOT NECESSARILLY congruent. This is why there is no Side Side Angle (SSA) and there is no Angle Side Side (ASS) postulate. However, if you would like a picture to illustrate why there is no ASS or SSA postulate look at the two triangles below. As you can see, even though side BC = BD , this side length is able to swivel such that two non congruent triangles are created even though they have two congruent sides and a congruent, non included angle. The two triangles are NOT congruent
D - Sample Size Calculator 1 This Sample Size Calculator is presented as a public service of Creative Research Systems survey software. You can use it to determine how many people you need to interview in order to get results that reflect the target population as precisely as needed. You can also find the level of precision you have in an existing sample. Before using the sample size calculator, there are two terms that you need to know. Enter your choices in a calculator below to find the sample size you need or the confidence interval you have. Sample Size Calculator Terms: Confidence Interval & Confidence Level The confidence interval (also called margin of error) is the plus-or-minus figure usually reported in newspaper or television opinion poll results. The confidence level tells you how sure you can be. When you put the confidence level and the confidence interval together, you can say that you are 95% sure that the true percentage of the population is between 43% and 51%. Sample sizePercentagePopulation size
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SS - Geometry 2007 Sign In | My Account | HMHEducation | eServices | Online Store | Contact Us | FAQ Find another book Search: Geometry, 2007 Help With the Math Practice, Practice, Practice Games and Activities Animated Math Animations Quick Reference Assessment D - Distribution Stem and Leaf Displays Author(s) David M. Lane Prerequisites Distributions Learning Objectives Create and interpret basic stem and leaf displays Create and interpret back-to-back stem and leaf displays Judge whether a stem and leaf display is appropriate for a given data set A stem and leaf display is a graphical method of displaying data. Table 1. A stem and leaf display of the data is shown in Figure 1. Figure 1. To make this clear, let us examine Figure 1 more closely. One purpose of a stem and leaf display is to clarify the shape of the distribution. We can make our figure even more revealing by splitting each stem into two parts. Figure 2. Figure 2 is more revealing than Figure 1 because the latter figure lumps too many values into a single row. There is a variation of stem and leaf displays that is useful for comparing distributions. Figure 3. Figure 3 helps us see that the two seasons were similar, but that only in 1998 did any teams throw more than 40 TD passes. Table 2. Figure 4.
SS - Similar Triangles Definitions and Problems Definition Generally, two triangles are said to be similar if they have the same shape, even if they are scaled, rotated or even flipped over. The mathematical presentation of two similar triangles A1B1C1 and A2B2C2 as shown by the figure beside is: Two triangles are similar if: 1. 2. 3. Be careful not to mix similar triangles with identical triangle. Therefore, all identical triangles are similar. Although the above shows that we need to know the measures of the three angles or the lengths of the three sides of each triangle in order to decide whether the two triangles are similar or not, it would be sufficient, for solving problems involving similar triangles, to know only three of the above measures for each triangle. 1) the three angles of each triangle (without the need to know the lengths of their sides). Or at least 2 angles of the first triangle are equal to 2 angles of the second triangle. 3) the lengths of two sides and the measure of one angle of each triangle. Solution:
D - When to Use Mean, Median, or Mode When not to use the mean The mean has one main disadvantage: it is particularly susceptible to the influence of outliers. These are values that are unusual compared to the rest of the data set by being especially small or large in numerical value. For example, consider the wages of staff at a factory below: The mean salary for these ten staff is $30.7k. However, inspecting the raw data suggests that this mean value might not be the best way to accurately reflect the typical salary of a worker, as most workers have salaries in the $12k to 18k range. Another time when we usually prefer the median over the mean (or mode) is when our data is skewed (i.e., the frequency distribution for our data is skewed). Median The median is the middle score for a set of data that has been arranged in order of magnitude. We first need to rearrange that data into order of magnitude (smallest first): Our median mark is the middle mark - in this case, 56 (highlighted in bold). Mode
SS - Similar Triangles Applications Image Source: A powerful Zoom lens for a 35mm camera can be very expensive, because it actually contains a number of highly precise glass lenses, which need to be moved by a tiny motor into very exact positions as the camera auto focuses. The Geometry and Mathematics of these lenses is very involved, and they cannot be simply mass produced and tested by computer robots. Lots of effort required to manufacture these lenses results in their very high price tags. Here is a diagram showing how the zoom lens internal arrangement changes as we zoom from 18mmm wide angle to 200mm fully zoomed in: Image Source: Image Copyright 2013 by Passy’s World of Mathematics Shown above are some band photographs taken by Passy with a special low light camera. Unfortunately this camera does not have a zoom lens, and so you need to be right up close to the stage to take good pictures. Measuring heights of tall objects is also covered in this lesson. Bow Tie Triangles
D - Collecting and Analyzing Data What do we mean by collecting data?What do we mean by analyzing data?Why should you collect and analyze data for your evaluation?When and by whom should data be collected and analyzed?How do you collect and analyze data? In previous sections of this chapter, we’ve discussed studying the issue, deciding on a research design, and creating an observational system for gathering information for your evaluation. What do we mean by collecting data? Essentially, collecting data means putting your design for collecting information into operation. Recording and organizing data may take different forms, depending on the kind of information you’re collecting. Some of the things you might do with the information you collect include: There are two kinds of variables in research. What do we mean by analyzing data? Analyzing information involves examining it in ways that reveal the relationships, patterns, trends, etc. that can be found within it. Quantitative data Qualitative data Patterns. In Summary
SS - Congruent Triangles Definition: Triangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other. In the simple case below, the two triangles PQR and LMN are congruent because every corresponding side has the same length, and every corresponding angle has the same measure. The angle at P has the same measure (in degrees) as the angle at L, the side PQ is the same length as the side LM etc. Try this Drag any orange dot at P,Q,R. The other triangle LMN will change to remain congruent to it. In the diagram above, the triangles are drawn next to each other and it is obvious they are identical. Imagine the triangles are cardboard One way to think about triangle congruence is to imagine they are made of cardboard. How to tell if triangles are congruent Any triangle is defined by six measures (three sides, three angles). AAA does not work. They are called similar triangles (See Similar Triangles).
D - Likert Scale by Saul McLeod published 2008 Various kinds of rating scales have been developed to measure attitudes directly (i.e. the person knows their attitude is being studied). The most widely used is the Likert Scale. Likert (1932) developed the principle of measuring attitudes by asking people to respond to a series of statements about a topic, in terms of the extent to which they agree with them, and so tapping into the cognitive and affective components of attitudes. Likert-type or frequency scales use fixed choice response formats and are designed to measure attitudes or opinions (Bowling, 1997; Burns, & Grove, 1997). A Likert-type scale assumes that the strength/intensity of experience is linear, i.e. on a continuum from strongly agree to strongly disagree, and makes the assumption that attitudes can be measured. In it final form, the Likert Scale is a five (or seven) point scale which is used to allow the individual to express how much they agree or disagree with a particular statement.