Lesson Plan
EngageNY

Equations for Tangent Lines to Circles

For Teachers 9th - 12th Standards
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...
Lesson Plan
EngageNY

Tangent Lines and the Tangent Function

For Teachers 11th - 12th Standards
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...
Lesson Plan
Curated OER

Worksheet 7: Slope and Tangents

For Teachers 12th - Higher Ed
Providing both review and practice problems, this worksheet prompts students to answer five questions having to do with slope, tangents lines, graphing, the Squeeze Theorem, differentiable functions and derivatives. This activity could...
Lesson Plan
Curated OER

Tangent Lines and the Radius of a Circle

For Teachers 9th - 12th Standards
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. 
Lesson Plan
EngageNY

Properties of Tangents

For Teachers 9th - 12th Standards
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,...
Lesson Plan
EngageNY

The Inscribed Angle Alternate – A Tangent Angle

For Teachers 9th - 12th Standards
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...
Lesson Plan
EngageNY

Why Call It Tangent?

For Students 10th - 12th Standards
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...
Lesson Plan
Curated OER

Worksheet 10 - Limits

For Teachers Higher Ed
In this limits worksheets, students graph tangent lines and determine the slope of a secant line. This one-page worksheet contains six multi-step problems.
Lesson Plan
Texas Instruments

Exploring Tangents

For Teachers 9th - 12th Standards
Explore the concept of tangent lines. In this tangent line lesson plan, 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...
Lesson Plan
EngageNY

Tangent Segments

For Teachers 9th - 12th Standards
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...
Lesson Plan
Curated OER

Introduction to Tangent Lines using the TI-Nspire

For Teachers 9th - 11th
Students make mathematical argument using the concept of Limit. In this algebra lesson, student calculate the instantaneous rate of change from the linear graph. They use a TI-calculator to create a visual of the graphs.
Lesson Plan
Curated OER

Secant and Tangent Lines

For Teachers 12th
Twelfth graders recognize the use of the slope of the secant line and connect it with the graph of the secant line, as the secant line approaches the tangent line. They also recognize the two forms of the slope formula used and practice...
Lesson Plan
EngageNY

Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams

For Teachers 9th - 12th Standards
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...
Lesson Plan
Curated OER

Tangent Properties

For Teachers 9th - 12th
Students explore properties of tangent lines.  In this properties of tangent lines activity, students discuss the perpendicular relationship between a tangent line on a circle and the circle's radius.  Students use that...
Lesson Plan
Curated OER

Secant Line Approximation of the Tangent Line

For Teachers 9th - 11th
Students 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.
Lesson Plan
Curated OER

Interesting Properties of Cubic Functions to Discover Graphically or Numerically

For Teachers 9th - 12th Standards
Learners investigate the slope of a cubic function. They find the tangent line of the cubic function at point P, and discuss the relationship between point P and point Q, the point the tangent line intersects the cubic function. ...
Lesson Plan
EngageNY

Applying Tangents

For Students 9th - 10th Standards
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...
Lesson Plan
Curated OER

Implicit Differentiation

For Teachers 9th - 12th Standards
Pupils explore the concept of derivatives. They use implicit differentiation to determine points on a graph where a tangent line is horizontal, vertical, or oblique. Finally, learners find the derivative of a polynomial by...
Lesson Plan
Illustrative Mathematics

Two Wheels and a Belt

For Teachers 9th - 10th Standards
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...
Lesson Plan
EngageNY

Secant Lines; Secant Lines That Meet Inside a Circle

For Teachers 9th - 12th Standards
Young mathematicians identify different cases of intersecting secant lines. They then investigate the case where secant lines meet inside a circle.
Lesson Plan
Curated OER

Lines in the Plane

For Teachers 9th - 11th
Students differentiate between parallel and perpendicular lines. In this algebra lesson, students graph linear equations using the slope intercept form. They classify lines based on their slopes.
Lesson Plan
Texas Instruments

Drawing a Line Tangent to a Circle

For Teachers 9th - 12th Standards
Explore lines tangent to a circle. In this math lesson plan, students manipulate circles and lines on a TI calculator. They draw a circle  and analyze perpendicular lines intersecting the circle in only one place. This activity...
Lesson Plan
Curated OER

Worksheet 8 - Limit of Slopes

For Teachers Higher Ed
For this limit of slopes worksheet, students compute the limit of slopes, find the slope of the secant line, and determine the slope of the tangent line. This one-page worksheet contains five multi-step problems.
Lesson Plan
Curated OER

Secants, Tangents and Arcs

For Teachers 9th - 12th Standards
Students identify chords and angles. In this geometry lesson, students calculate the length of the chords inside and outside of-the circle. They differentiate between tangent and secant lines.

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