1.2.3 Basic Constructions
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This document outlines basic geometric constructions that will be taught in class, including constructing congruent segments, perpendicular bisectors to find midpoints, congruent angles, and angle bisectors using only a compass and straightedge. The objectives are to learn how to construct congruent segments, find midpoints using perpendicular bisectors, construct congruent angles, and construct angle bisectors.
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1) m + 14 < 4
-14 -14
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Graph: m < -10
2) -7 > y-1
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Graph: y < -6
3) (-3)k < 10(-3)
-3
k > -30
Graph: k > -30
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-x -x
x + 5 ≤ 1
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x ≤ -4
Graph: x ≤ -4
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For those who need help in PPT's for Lines and Angles and want to get good results.
Visit my website :- http://www.soumyamodakbed.blogspot.in/ for more information.
Angles ppt
1) The document defines an angle as being formed by two rays with a common endpoint called the vertex. Angles can have points in their interior, exterior, or on the angle.
2) There are three main ways to name an angle: using three points with the vertex in the middle, using just the vertex point when it is the only angle with that vertex, or using a number within the angle.
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This document discusses methods for solving inequalities, including:
1) Determining if a number is a solution of an inequality.
2) Graphing inequalities on a number line.
3) Using the addition principle and multiplication principle to solve inequalities algebraically, such as isolating the variable.
4) Applying the addition principle and multiplication principle together to solve more complex inequalities.
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- Points, lines, planes, and space as the building blocks of geometry.
- Definitions of key terms like points, lines, rays, segments, planes, angles, and different types of angles.
- How to measure angles using a protractor and the units of degrees.
- Relationships between geometric figures like parallel and intersecting lines, coplanar points and lines, and different types of angles.
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This document discusses how to graph and solve quadratic inequalities in one and two variables. It provides examples of graphing quadratic inequalities by drawing the parabola, choosing a test point, and shading the appropriate region. Systems of quadratic inequalities can be graphed on the same grid, with the shared shaded region representing the solutions. Quadratic inequalities in one variable can also be solved by graphing the parabola and identifying the x-values where it lies above or below the x-axis, or algebraically by solving the inequality as an equation and testing values between the solutions.
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Nth roots can be expressed using rational exponents, where the denominator of the exponent is the index of the radical. To evaluate expressions with rational exponents, one should rewrite them in radical form, evaluate the radical, and then raise the expression to the power indicated by the original exponent. Examples are provided of evaluating various expressions with rational exponents.
Inequalities ppt revised
Here are the steps to solve each inequality and graph the solution:
1) m + 14 < 4
-14 -14
m < -10
Graph: m < -10
2) -7 > y-1
+1 +1
-6 > y
y < -6
Graph: y < -6
3) (-3)k < 10(-3)
-3
k > -30
Graph: k > -30
4) 2x + 5 ≤ x + 1
-x -x
x + 5 ≤ 1
-5 -5
x ≤ -4
Graph: x ≤ -4
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This document discusses various theorems and properties related to triangles. It explains the Basic Proportionality Theorem, also known as Thales' Theorem, which states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. It also covers similarity criteria like AAA, SSA, and SSS. The Area Theorem demonstrates that the ratio of areas of similar triangles equals the square of the ratio of corresponding sides. Additionally, it proves Pythagoras' Theorem, which relates the sides of a right triangle, and its converse. In summary, the document outlines key triangle theorems regarding proportional division, similarity, areas, and the Pythagorean relationship between sides.
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This document discusses how to solve absolute value equations and inequalities. It explains that absolute value equations can have two solutions that come from setting the expression equal to the number or its opposite. It provides examples of solving equations of the form |ax + b| = c by writing it as two separate equations. The document also explains how to solve absolute value inequalities by rewriting them as compound inequalities using "and" or "or", depending on whether the inequality sign is < or >, and then solving the resulting inequalities.
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This document provides an overview of solving absolute value equations and inequalities. It explains that absolute value is the distance from 0 on the number line. For absolute value equations, two problems must be set up: one leaving everything as is without bars, and one leaving what's inside bars the same but changing the sign outside. Examples are provided of solving basic absolute value equations and inequalities, which require isolating the absolute value bars first before setting up two equations or problems. Practice problems are included for the reader to work through.
Alg II 3-2 Solving Systems Algebraically
This document provides an overview of solving systems of linear equations algebraically. There are two main methods: substitution and elimination. Substitution involves isolating one variable and substituting it into the other equation. Elimination involves adding or subtracting equations to eliminate one variable. Examples are provided to demonstrate both methods. The objectives are for students to be able to solve linear systems algebraically and relate it to representing relationships between quantities with graphs and equations.
The angles family
The document introduces the Angle family, consisting of Mr. Obtuse Angle, Mrs. Right Angle, Baby Acute Angle, and their pet Reflex Angle. Mr. Obtuse Angle is always inside and measures between 90 and 180 degrees. Mrs. Right Angle always measures 90 degrees and believes she is always right. Baby Acute Angle is the smallest family member and loves hugs. Reflex Angle is their pet dog who is currently 180 degrees but can grow to 360 degrees, making him the biggest angle.
Lines and angles
For those who need help in PPT's for Lines and Angles and want to get good results.
Visit my website :- http://www.soumyamodakbed.blogspot.in/ for more information.
Angles ppt
1) The document defines an angle as being formed by two rays with a common endpoint called the vertex. Angles can have points in their interior, exterior, or on the angle.
2) There are three main ways to name an angle: using three points with the vertex in the middle, using just the vertex point when it is the only angle with that vertex, or using a number within the angle.
3) There are four types of angles: acute, right, obtuse, and straight. Angles are measured in degrees with a full circle being 360 degrees.
Solution of linear equation & inequality
The document discusses solving linear equalities and inequalities with one variable. It defines key terms like equations, inequalities, and linear equations. It then provides steps for solving different types of linear equations and inequalities by collecting like terms, adding/subtracting the variable term to one side, and multiplying/dividing both sides by constants. The document also explains how to graph solutions to inequalities on a number line, indicating open and closed circles based on the inequality symbols. Examples are provided of solving and graphing various linear equalities and inequalities with one variable.
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The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
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IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
HIGHLIGHTS ON HEALTH EDUCATION.
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Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"
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1.2.3 Basic Constructions
- 1. Basic Constructions Objectives: • Construct congruent segments • Construct a perpendicular bisector and find the midpoint • Construct congruent angles • Construct an angle bisector
- 2. constructionconstructionconstructionconstruction – a method of geometric drawing that uses only a compass and a straightedge. Constructing a figure is different from just sketching it. Construction has been used since ancient times both in philosophical and practical areas. In class, you will learn to construct • congruent segments • segment midpoints • segment bisectors • congruent angles • angle bisectors