About This Chapter
Lines & Circles - Chapter Summary
Benefit from the expertise of top instructors who have created fun lessons you can use to better understand lines and circles. Access these lessons in a secure online environment using your computer, smartphone or tablet. Ensure you fully comprehend the geometric principles of straight lines, pairs of straight lines and circles. In no time, you will be ready to:
- Define straight lines and concurrent lines
- List the properties of concurrent lines in a triangle
- Share the definition and theorem associated with linear pairs
- Recognize parallel, perpendicular and transverse lines
- Use the angle bisector theorem, and find the point of intersection graphically and algebraically
- Explain what makes a circle a conic section, and calculate the circumference of a circle
- Find the equation of a circle
- Exhibit an understanding of the tangent of a circle and chord theorems of circles
Study lines and circles your way by accessing any number of lessons in this chapter in the sequence and at the frequency you desire. Before, during or after reviewing the lessons, assess your comprehension by taking multiple-choice quizzes. Submit any questions you have about topics covered in this chapter to our experts. Make sure you understand all of the lessons by taking the practice chapter exam.
1. What is a Straight Line? - Definition & Examples
In this lesson, you will learn the definition and properties of a straight line. You will be given plenty of examples to ensure your understanding of straight lines. Following the lesson will be a brief quiz to test your new knowledge.
2. What Are Concurrent Lines? - Definition & Examples
Lines that all meet at a point have a very special name. The point where all of those lines meet also has a special name. In this lesson we'll learn all about concurrent lines and how they intersect.
3. Properties of Concurrent Lines in a Triangle
Centroids, orthocenters, incenters, circumcenters, oh my! Don't worry though. In this lesson, we master the various terms for concurrent lines in triangles and match them to altitudes, angle bisectors, perpendicular bisectors and medians.
4. Linear Pair: Definition, Theorem & Example
In this lesson, we'ill discuss how a linear pair is formed and what characteristics apply to angles that create a linear pair. We'lll also go through a few examples in which we solve for the missing angle. At the end of the lesson, test yourself with a quiz.
5. Parallel, Perpendicular and Transverse Lines
What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.
6. Angle Bisector Theorem: Definition and Example
Watch this video lesson and learn how you can use the angle bisector theorem to help you find the lengths of missing sides. Also learn how you can identify an angle bisector just by looking at the lengths of the sides of a triangle.
7. Point of Intersection: Definition & Formula
In this lesson, we'll learn what the point of intersection is and how to find it graphically and algebraically. This concept applies to lots of other areas of study, including business, finance, construction and physics.
8. The Circle: Definition, Conic Sections & Distance Formula
Watch this video lesson, and you will learn what makes a circle a conic section. Also learn how to calculate the circumference of a circle. You will learn about the one important measurement that you need for any circle.
9. How to Find the Equation of a Circle
There are two commonly used forms of equations for a circle, in this lesson we'll take a few minutes to examine and understand both forms, and be able to convert from one to the other.
10. Tangent of a Circle: Definition & Theorems
What happens when a line just barely touches a circle? It's a tangent! In this lesson, we'll learn all about tangents to circles, including a few key theorems. We'll also look at tangent circles.
11. Chord Theorems of Circles in Geometry
Watch this video lesson to learn how a radius will always bisect a perpendicular chord and how equidistant chords will always be congruent to each other. Also, see an example of how you can use these two theorems.
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Other chapters within the AP EAMCET E (Engineering): Study Guide & Test Prep course
- Principles of Mathematical Functions
- Mathematical Induction
- Overview of Matrices
- Overview of Complex Numbers
- Understanding Quadratic Expressions
- Theory of Equations
- Permutations & Combinations in Algebra
- Understanding the Binomial Theorem
- Understanding Partial Fractions
- Fundamental Elements of Trigonometry
- Understanding Hyperbolic Functions
- Trigonometric Properties of Triangles
- Vector Algebra
- Measures of Dispersion
- Principles of Probability
- Coordinate Geometry Overview
- Conic Sections Overview
- Three-Dimensional Coordinates
- Limits & Continuity
- Differentiation in Calculus
- Integration in Calculus
- Understanding Differential Equations
- Understanding the Basics of Physics
- Units & Measurement in Physics
- Understanding Motion in Physics
- Systems of Particles & Rotational Motion
- Work, Energy & Power Overview
- Overview of Oscillations
- Overview of Gravitation
- Properties of Solids, Fluids & Gases
- Thermal Properties of Matter
- Rays, Waves & Wave Optics
- Understanding Electricity
- Magnetic Force & Electromagnetism
- Currents, Waves & Circuits
- Communication Systems
- Atoms & Nuclei
- Atomic Structure Overview
- Understanding Elements & the Periodic Table
- Chemical Bonding & Molecular Structure
- States of Matter in Chemistry
- Basic Stoichiometry
- Thermodynamics & Chemistry
- Chemical Equilibrium & Acid-Bases
- Hydrogen & Hydrogen Compounds
- Alkali & Alkaline Earth Metals
- Environmental Chemistry
- Understanding Organic Chemistry
- Solids in Chemistry
- Electrochemistry & Chemical Kinetics
- Surface Chemistry
- Metallurgy Overview
- Polymers Overview
- Understanding Biomolecules
- Everyday Chemistry
- AP EAMCET E (Engineering) Flashcards