PPT-Proportions in Triangles

Review Midsegment Theorem Review Midsegment Theorem See the two triangles What if we compared corresponding sides with proportions 40x 2560 x 64   This is todays lesson. Written by: Jack S. . Calcut. Presented by: Ben Woodford. (pay attention: there Will be a test at the end). Definitions. An . angle is . rational . provided it is commensurable with a straight . angle; equivalently. In this section we will be able to give real life examples of Fractions and Proportions. We will also learn how to solve and evaluate Fractions and Proportions in word problems.. Lesson plan goals. We are constantly using fractions everyday. Most of the time not really even noticing that we are using fractions. Have you ever checked the clock or a watch for the time? Guess what the time is a fraction of a day so any time you use a watch, clock. Proportions. What are proportions?. - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures.. What do we mean by similar?. - Similar describes things which have the same shape but are not the same size.. Statistics. What you will learn. Be able to state the null and alternative hypotheses for testing the difference between two population proportions.. Know how to examine your data for violations of conditions that would make inference about the difference between the two population proportions unwise or invalid.. two-proportion inference tests. Chapter 22. Proportions observed in independent random samples . are. independent. Thus, we can add their variances. So…. The standard deviation of the difference between two sample proportions is . Difference Between Proportions. Sometimes we want to see if there is a significant difference between independent groups.. Control group vs. treatment group or placebo group. Men vs. women. Last year vs. this year. Yawn Seed?. Subject. Yawned?. Yes. No. Total. Yes. 10. 4. 14. No. 24. 12. 36. Total. 34. 16. 50. Trial. Number who yawned in yawn seed group. Number who yawned in no yawn seed group. Difference in proportions (yawn. Using Congruent Triangles. Congruent triangles have congruent corresponding parts. So, if you can prove the two triangles are congruent then you know their corresponding parts must be congruent as well.. Watch for Parallel Lines,. Transversals, and. Angle Bisectors.  . Side Splitter Theorem. (related to . Midsegment. . Theorem). If a line is parallel to ONE side of a triangle AND intersects the other two sides, then it divides those other TWO sides proportionally.. Lewis Carroll/Charles Dodgson. Some . fun facts:. .. as a mathematician, Dodgson was, in the words of . . Peter Heath: "An inveterate publisher of trifles [who] was forever putting out pamphlets, papers, broadsheets, and books on mathematical topics [that] earned him no reputation beyond that of a crotchety, if sometimes amusing, controversialist, a compiler of puzzles and curiosities, and a busy yet ineffective reformer on elementary points of computation and instructional method. In the higher reaches of the subject he made no mark at all, and has left none since." . Proportion – Learning Outcomes Express quantities as proportions of each other using fractions, decimals, ratios, and percentages. Divide quantities into a given proportion. Express errors as a proportion. Proportions and Similar Figures What is Similarity? Not Similar Similar Similar Not Similar Similar Triangles Similar Figures Figures that have the same shape but not necessarily the same size are Magic Triangles. There are 3 magic triangles, two of which are on your formula sheet. They let you do some trigonometric equations without calculators. These are a fundamental part of ”exact solutions” . Alan. Edelman. Mathematics . Computer Science & AI Labs. Gilbert . Strang. Mathematics. Computer Science & AI Laboratories. Page . 2. A note passed during a lecture. Can you do. this integral in R.