1.2.2 Pairs of Angles
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Identify linear pairs, vertical angles, complementary angles, and supplementary angles, and use their relationships to set up and solve equations.
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1.2.3 Pairs of Angles
This document defines and provides examples of linear pairs, vertical angles, complementary angles, and supplementary angles. It explains that linear pairs are two adjacent angles with a common vertex and side but no interior points, vertical angles are nonadjacent angles formed by two intersecting lines that are always congruent, complementary angles have a sum of 90 degrees, and supplementary angles have a sum of 180 degrees. The document includes practice problems asking to identify missing angle measures using properties of these angle relationships.
Pairs of Angles
This document defines and describes different types of angles:
1) Adjacent angles share a common vertex and side. Vertically opposite angles are formed when two lines intersect and are equal.
2) Complementary angles have a sum of 90 degrees. Supplementary angles have a sum of 180 degrees.
3) A linear pair is two adjacent supplementary angles.
4) A transversal intersects two or more lines. It forms corresponding, alternate, and interior angles that follow specific properties.
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Two angles are complementary if their measures sum to 90 degrees. Two angles are supplementary if their measures sum to 180 degrees. Adjacent angles have a common vertex and one common side but no interior points in common, such as the angles formed by scissors. Vertically opposite angles are formed without a common side when two lines intersect. A linear pair is formed when the non-common sides of adjacent angles lie in a straight line. A transversal is a line that intersects two or more other lines at distinct points, and intersecting lines cut each other at a common point.
Solve Lines and Angles Question Paper for CBSE Class 9
Get all the NCERT solutions for class 9 mathematics at Extramarks. Students studying with NCERT Textbook to study Maths, then you must come across the question papers. Once you have finished the lesson, you must be looking for a solution to these exercises. Extramarks provides complete NCERT Solutions for CBSE Lines and Angles for Class 9 question paper in one place. Visit the Extramarks site for more modules and subjects for NCERT solutions.
Section 5
This document defines and describes different types of angle relationships: adjacent angles share a vertex and side; vertical angles are nonadjacent angles formed by two intersecting lines and are congruent; a linear pair are adjacent angles with noncommon opposite rays; complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees; and perpendicular lines intersect to form four right angles and congruent adjacent angles.
Parallel Line Properties
If parallel lines are cut by a transversal, then:
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent
- Interior angles on the same side of the transversal are supplementary
- Exterior angles on the same side of the transversal are supplementary
Linear pair
1. The document discusses linear pairs of angles and how to determine if two angles form a linear pair.
2. It provides examples of drawing angles and labeling common and uncommon sides to identify linear pairs. Properties of linear pairs are explained, including that angles in a linear pair are supplementary.
3. Analyze statements about linear pairs and determine if they are always, sometimes, or never true. Solve word problems involving finding missing angle measures in linear pairs.
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This document discusses different ways to prove that two lines are parallel using properties of parallel lines cut by a transversal. It introduces the converse theorems for corresponding angles, alternate interior angles, consecutive interior angles, and alternate exterior angles being congruent to show lines are parallel. It also presents two additional theorems: if two lines are parallel to the same line then they are parallel to each other, and if two lines are perpendicular to the same line then they are parallel to each other. The document provides example problems and homework assignments to practice these concepts.
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This document defines and provides examples of linear pairs, vertical angles, complementary angles, and supplementary angles. It explains that linear pairs are two adjacent angles with a common vertex and side but no interior points, vertical angles are nonadjacent angles formed by two intersecting lines that are always congruent, complementary angles have a sum of 90 degrees, and supplementary angles have a sum of 180 degrees. The document includes practice problems asking to identify missing angle measures using properties of these angle relationships.
Pairs of Angles
This document defines and describes different types of angles:
1) Adjacent angles share a common vertex and side. Vertically opposite angles are formed when two lines intersect and are equal.
2) Complementary angles have a sum of 90 degrees. Supplementary angles have a sum of 180 degrees.
3) A linear pair is two adjacent supplementary angles.
4) A transversal intersects two or more lines. It forms corresponding, alternate, and interior angles that follow specific properties.
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Two angles are complementary if their measures sum to 90 degrees. Two angles are supplementary if their measures sum to 180 degrees. Adjacent angles have a common vertex and one common side but no interior points in common, such as the angles formed by scissors. Vertically opposite angles are formed without a common side when two lines intersect. A linear pair is formed when the non-common sides of adjacent angles lie in a straight line. A transversal is a line that intersects two or more other lines at distinct points, and intersecting lines cut each other at a common point.
Solve Lines and Angles Question Paper for CBSE Class 9
Get all the NCERT solutions for class 9 mathematics at Extramarks. Students studying with NCERT Textbook to study Maths, then you must come across the question papers. Once you have finished the lesson, you must be looking for a solution to these exercises. Extramarks provides complete NCERT Solutions for CBSE Lines and Angles for Class 9 question paper in one place. Visit the Extramarks site for more modules and subjects for NCERT solutions.
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This document defines and describes different types of angle relationships: adjacent angles share a vertex and side; vertical angles are nonadjacent angles formed by two intersecting lines and are congruent; a linear pair are adjacent angles with noncommon opposite rays; complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees; and perpendicular lines intersect to form four right angles and congruent adjacent angles.
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If parallel lines are cut by a transversal, then:
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- Interior angles on the same side of the transversal are supplementary
- Exterior angles on the same side of the transversal are supplementary
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here is a ppt of lines and angles class 9th
you can watch it and please comment on it
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here is a ppt of lines and angles class 9th
you can watch it and please comment on it
thanxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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More Free Resources to Help You Teach your Geometry Lesson on Exploring Angle Pairs can be found here:
*** https://geometrycoach.com/exploring-angle-pairs/
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Lines and angles class 9 ppt made by hardik kapoor
Lines and angles class 9 ppt made by hardik kapoor
linesandangles-111014002441-phpapp02-150823071910-lva1-app6892 (1).pptx
linesandangles-111014002441-phpapp02-150823071910-lva1-app6892 (1).pptx
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6.7 Exponential and Logarithmic Models
* Model exponential growth and decay
* Use Newton's Law of Cooling
* Use logistic-growth models
* Choose an appropriate model for data
* Express an exponential model in base e
4.5 Special Segments in Triangles
* Construct perpendicular and angle bisectors
* Use bisectors to solve problems
* Identify the circumcenter and incenter of a triangle
* Use triangle segments to solve problems
1.4 Conditional Statements
* Identify, write, and analyze conditional statements
* Write the inverse, converse, and contrapositive of a conditional statement
* Write a counterexample to a fake conjecture
1.3 Distance and Midpoint Formulas
* Find the distance between two points
* Find the midpoint of two given points
* Find the coordinates of an endpoint given one endpoint and a midpoint
* Find the coordinates of a point a fractional distance from one end of a segment
1.5 Quadratic Equations.pdf
This document provides instruction on factoring polynomials and quadratic equations. It begins by reviewing factoring techniques like finding the greatest common factor and factoring trinomials and binomials. Examples are provided to demonstrate the factoring methods. The document then discusses solving quadratic equations by factoring, putting the equation in standard form, and setting each factor equal to zero. An example problem demonstrates solving a quadratic equation through factoring. The document concludes by assigning homework and an optional reading for the next class.
3.2 Graphs of Functions
* Connect functions to their graphs
* Graph piecewise-defined functions
* Graph absolute value functions
* Graph greatest-integer functions
* Interpret graphs
* Use the vertical line test to determine a function
3.2 Graphs of Functions
* Connect functions to their graphs
* Graph piecewise-defined functions
* Graph absolute value functions
* Graph greatest-integer functions
* Interpret graphs
* Use the vertical line test to determine a function
3.1 Functions
* Introduce functions and function notation
* Develop skills in constructing and interpreting the graphs of functions
* Learn to apply this knowledge in a variety of situations
2.5 Transformations of Functions
* Recognize graphs of common functions.
* Graph functions using vertical and horizontal shifts.
* Graph functions using reflections about the x-axis and the y-axis.
* Graph functions using compressions and stretches.
* Combine transformations.
2.2 More on Functions and Their Graphs
This document discusses functions and their graphs. It defines increasing, decreasing and constant functions based on how the function values change as the input increases. Relative maxima and minima are points where a function changes from increasing to decreasing. Symmetry of functions is classified by the y-axis, x-axis and origin. Even functions are symmetric about the y-axis, odd functions are symmetric about the origin. Piecewise functions have different definitions over different intervals.
1.6 Other Types of Equations
This document provides examples and steps for solving various types of equations beyond linear equations, including:
1) Polynomial equations solved by factoring
2) Equations with radicals where radicals are eliminated by raising both sides to a power
3) Equations with rational exponents where both sides are raised to the reciprocal power
4) Equations quadratic in form where an algebraic substitution is made to transform into a quadratic equation
5) Absolute value equations where both positive and negative solutions must be considered.
1.5 Quadratic Equations (Review)
This document provides instruction on factoring quadratic equations. It begins by reviewing factoring polynomials and trinomials. It then discusses factoring binomials using difference of squares, sum/difference of cubes, and other patterns. Finally, it explains that a quadratic equation can be solved by factoring if it can be written as a product of two linear factors. An example demonstrates factoring a quadratic equation by finding the two values that make each factor equal to zero.
2.1 Basics of Functions and Their Graphs
This document provides an overview of functions and their graphs. It defines what constitutes a function, discusses domain and range, and how to identify functions using the vertical line test. Key points covered include:
- A function is a relation where each input has a single, unique output
- The domain is the set of inputs and the range is the set of outputs
- Functions can be represented by ordered pairs, graphs, or equations
- The vertical line test identifies functions as those where a vertical line intersects the graph at most once
- Intercepts occur where the graph crosses the x or y-axis
9.6 Binomial Theorem
The document discusses the binomial theorem, which provides a formula for expanding binomial expressions of the form (a + b)^n. It gives the formula for finding the coefficient of the term containing b^r as nCr. Several examples are worked out applying the binomial theorem to expand binomial expressions and find specific terms. Factorial notation is introduced for writing the coefficients. The document also discusses using calculators and Desmos to evaluate binomial coefficients. Practice problems are assigned from previous sections.
13.3 Venn Diagrams & Two-Way Tables
The document discusses using Venn diagrams and two-way tables to organize data and calculate probabilities. It provides examples of completing Venn diagrams and two-way tables based on survey data about students' activities. It then uses the tables and diagrams to calculate probabilities of different outcomes. The examples illustrate how to set up and use these visual representations of categorical data.
13.2 Independent & Dependent Events
* Identify events as independent or dependent
* Calculate the probabilities of independent and dependent events
9.5 Counting Principles
* Solve counting problems using the Addition Principle.
* Solve counting problems using the Multiplication Principle.
* Solve counting problems using permutations involving n distinct objects.
* Solve counting problems using combinations.
* Find the number of subsets of a given set.
* Solve counting problems using permutations involving n non-distinct objects.
13.1 Geometric Probability
* Calculate geometric probabilities
* Use geometric probability to predict results in real world situations.
9.4 Series and Their Notations
* Use summation notation.
* Use the formula for the sum of the first n terms of an arithmetic series.
* Use the formula for the sum of the first n terms of a geometric series.
* Use the formula for the sum of an infinite geometric series.
* Solve annuity problems.
9.3 Geometric Sequences
* Find the common ratio for a geometric sequence.
* List the terms of a geometric sequence.
* Use a recursive formula for a geometric sequence.
* Use an explicit formula for a geometric sequence.
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1.2.2 Pairs of Angles
- 1. Pairs of Angles Objectives: The student will be able to (I can): Identify • linear pairs • vertical angles • complementary angles • supplementary angles and use these relationships to set up and solve equations.
- 2. adjacent anglesadjacent anglesadjacent anglesadjacent angles – two angles in the same plane with a common vertex and a common side, but no common interior points. Example: ∠1 and ∠2 are adjacent angles. linear pairlinear pairlinear pairlinear pair – two adjacent angles whose noncommon sides are opposite rays. (They form a line.) Example: 1 2
- 3. vertical anglesvertical anglesvertical anglesvertical angles – two nonadjacent angles formed by two intersecting lines. They are always congruent.They are always congruent.They are always congruent.They are always congruent. Example: ∠1 and ∠4 are vertical angles ∠2 and ∠3 are vertical angles 1 2 3 4
- 4. complementary anglescomplementary anglescomplementary anglescomplementary angles – two angles whose measures have the sum of 90°. supplementary anglessupplementary anglessupplementary anglessupplementary angles – two angles whose measures have the sum of 180°. ∠A and ∠B are complementary. (55+35) ∠A and ∠C are supplementary. (55+125) A 55° B 35° C 125°
- 5. Practice 1. What is m∠1? 2. What is m∠2? 3. What is m∠3? 1 60˚ 51˚ 2 105˚ 3
- 6. Practice 1. What is m∠1? 180 – 60 = 120˚ 2. What is m∠2? 90 – 51 = 39˚ 3. What is m∠3? 105˚ 1 60˚ 51˚ 2 105˚ 3