The document discusses the triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. It provides examples of using the triangle inequality to determine the possible length of the third side of a triangle given the lengths of two sides. Specifically, it shows how to set up inequalities and determine the range of possible values for the third side.
Define the sine, cosine, and tangent ratios and their inverses
Find the measure of a side given a side and an angle
Find the measure of an angle given two sides
Use trig ratios to solve problems
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. Area is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object
Define the sine, cosine, and tangent ratios and their inverses
Find the measure of a side given a side and an angle
Find the measure of an angle given two sides
Use trig ratios to solve problems
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. Area is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object
This learner modules talks about the Triangle Inequality. It also talks about the theorems & postulates that supports triangle inequalities in one or two triangles.
Triangle Inequality Theorem: Activities and Assessment MethodsMarianne McFadden
A comprehensive lesson on the Triangle Inequality Theorem, including pre-assessment, a hands-on activity (with rubric), and post-assessment methods that measure varying levels of achievement.
Palestine last event orientationfvgnh .pptxRaedMohamed3
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Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
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Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
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This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
4. Problem#1 The lenghts of two sides are 6 and 3. The length of the three side may be: To solve this question first you have to follow this easy steps: Step1: Add 6 and 3 which gives you 9 and 9 would be the higher range 6 3 x Step 2: Then you subtract 6 and 3 which gives you 3, 3 would be the lower range Step 3: Write an inequality with x Step 4Add the lower and higher range to the inequality **So then the inequality would be 9<x<3** The possible answer for x could be between 3 and 6 Credit-Erika Zumba
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6. Problem #3 The direct distance between city A and city B is 200 miles. The direct distance between city B and city C is 300 miles. Which could be the direct distance between city C and city A . So lets analyze the question: They are saying that between A and B is 200 miles. And they are also saying that between B and C is 300 miles. They want to know that what could be the distance between A and C. A B C 300 miles 200 miles First add 200 miles and 300 miles and you get 500 miles, 50 would be the higher range Then subtract 300 miles with 200 miles and you get 100, 100 would be the lower range After that, write an inequality with x, because x is the distance between A and C Then add the 100 in the left side of the x and the 500 to the right of the x Mutiple Choice 1) 50 miles 2) 350 miles 3) 550 miles 4) 650 miles The inequality would like this 100<x<500 The possible answer could be between 100 and 500 So now look at the possible answers one of them is 50 miles but that the less than 100.The other choice is 550 miles but that answer is greater than 500, and so is 650. So that only leaves us with 350 being the answer. Answer:350 miles x Credit-Ms.Mui
![Triangle Inequality ,[object Object]](https://image.slidesharecdn.com/triangleinequalitysides-111126195945-phpapp01/85/Triangle-inequality-sides-1-320.jpg)
