EngageNY
Equations for Tangent Lines to Circles
Don't go off on a tangent while writing equations of tangent lines! Scholars determine the equations for tangent lines to circles. They attempt both concrete and abstract examples, such as a tangent line to the unit circle through (p, 0).
CK-12 Foundation
Tangent Line Approximation: Estimating Square Roots
Estimating a square root is as easy as evaluating a linear equation. Using the derivative of the square root function, pupils calculate an estimation of square roots. Class members determine the equation of the tangent line at the value...
EngageNY
Tangent Lines and the Tangent Function
Construct tangent lines and make the connection to tangent functions. An informative lesson reviews the geometry origins of the tangent function. Pupils use that information to determine how to construct a tangent to a circle from a...
EngageNY
The Inscribed Angle Alternate – A Tangent Angle
You know the Inscribed Angle Theorem and you know about tangent lines; now let's consider them together! Learners first explore angle measures when one of the rays of the angle is a tangent to a circle. They then apply their newfound...
Curated OER
Tangent Lines and the Radius of a Circle
Your Geometry learners will collaboratively prove that the tangent line of a circle is perpendicular to the radius of the circle. A deliberately sparse introduction allows for a variety of approaches to find a solution.
EngageNY
Properties of Tangents
You know about the tangent function, but what are tangent lines to a circle? Learners investigate properties of tangents through constructions. They determine that tangents are perpendicular to the radius at the point of tangency, and...
CK-12 Foundation
Slope of a Tangent Line: Slope of the Tangent and Secant Lines
Learn to find the slope through a single point. The interactive provides a visualization of how to find the slope of a tangent line. With the aid of the visualization, pupils see the definition of the derivative in action. Class members...
EngageNY
Why Call It Tangent?
Discover the relationship between tangent lines and the tangent function. Class members develop the idea of the tangent function using the unit circle. They create tables of values and explore the domain, range, and end behavior of the...
Curated OER
Tangent Lines
In this tangent lines worksheet, 10th graders solve and complete 13 various types of problems. First, they solve the right triangles for the variables shown. Then, students name a radius, a diameter, a tangent, a secant, a point of...
EngageNY
Tangent Segments
What's so special about tangents? Learners first explore how if a circle is tangent to both rays of an angle, then its center is on the angle bisector. They then complete a set of exercises designed to explore further properties and...
Texas Instruments
Exploring Tangents
Explore the concept of tangent lines. In this tangent line lesson, learners graph a circle and two lines on their graphing calculator using Cabri Jr. Students construct the lines so that they both intersect at a given point and are both...
EngageNY
Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams
First angle measures, now segment lengths. High schoolers first measure segments formed by secants that intersect interior to a circle, secants that intersect exterior to a circle, and a secant and a tangent that intersect exterior to a...
Illustrative Mathematics
Tangent to a Circle From a Point
Learners see application of construction techniques in a short but sophisticated problem. Combining the properties of inscribed triangles with tangent lines and radii makes a nice bridge between units, a way of using information about...
EngageNY
Applying Tangents
What does geometry have to do with depression? It's an angle of course! Learners apply the tangent ratio to problem solving questions by finding missing lengths. Problems include angles of elevation and angles of depression. Pupils make...
Curated OER
Secant Line Approximation of the Tangent Line
Pupils perform operation with secant and tangent lines. In this calculus lesson, students find the derivative and relate it to the slope of a line. They differentiate between secant and tangent as they intersect a circle, using Cabri.
CK-12 Foundation
Vectors as Directed Line Segments: Directed Line Segment
Direct your class' attention to directed line segments. The interactive resource allows pupils to create segments with specific endpoints. Scholars plot the initial and terminal points to determine the direction and magnitude of the...
CK-12 Foundation
Absolute Versus Local Extrema
Get the class to take an extreme look at functions. The interactive presents a function on a closed interval with a movable tangent line. Using the given function, pupils determine the extrema, critical points, and points of inflection.
CK-12 Foundation
Average and Instantaneous Rates of Change
How can you determine the rate of change on a curve? Pupils use the interactive to discover what happens with the average rate of change as the point move closer to the other. Using the definition of the derivative, learners find that it...
Curated OER
Tangents, Secants, and Chords
In this tangents, secants and chords worksheet, 10th graders identify and solve 48 different problems that include using 3 different theorems for defining circles. First, they determine the area of each circle with C as the center and a...
Illustrative Mathematics
Two Wheels and a Belt
Geometry gets an engineering treatment in an exercise involving a belt wrapped around two wheels of different dimensions. Along with the wheels, this belt problem connects concepts of right triangles, tangent lines, arc length, and...
EngageNY
Secant Lines; Secant Lines That Meet Inside a Circle
Young mathematicians identify different cases of intersecting secant lines. They then investigate the case where secant lines meet inside a circle.
CK-12 Foundation
Newton's Method
Use an iterative process to find an approximation of a square root. Pupils use the interactive to find an approximation to find the positive root of a quadratic function with Newton's method. With the graphs, learners position the...
CK-12 Foundation
Directed Line Segments: Dog Park
Its a dog's world! Using a vector in standard position, pupils model the path a dog takes to different items in a dog park. The individuals use the interactive to find the magnitude and direction of the directed line segment.
EngageNY
Geometry Module 5: End-of-Module Assessment
The lessons are complete. Learners take an end-of-module assessment in the last installment of a 23-part module. Questions contain multiple parts, each assessing different aspects of the module.