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Constructing and Using Tangent Lines

Answer Keys Here

Aligned To Common Core Standard:

Circles - HSG-C.A.4

What are Tangent Lines? When dealing with circles and curves, there are a lot of different lines that kids need to know about, including chords, radius, diameter, secant, and tangents. The concept of tangent lines is a very useful one in the branch of calculus. It helps in magnifying the instantaneous slope of a curve. A line that touches the circumference of the circle or a curve at a single point, throughout its infinite length, it is called a tangent line. The slope of the tangent line is, and the instantons slope of a curve or circle are the same. A tangent line is always perpendicular to the radius of the circle. A tangent line helps in the approximation of a curve at one point as both the curve as well as the line are almost the same at the point of intersection. This series of worksheets and lessons helps students learn how to create their own tangent lines to better understand a plane curves and other geometric shapes.

Printable Worksheets And Lessons

Homework Sheets

What to do with those pesky triangles that stick outside of the circle.

  • Homework 1 - Since QR is tangent to P, QR is perpendicular to PQ. So PQR is a right triangle with hypotenuse PR.
  • Homework 2 - MP is the hypotenuse so go after the PT!
  • Homework 3 - Understanding where to take this to is important.

Practice Worksheets

I actually used this exact type of skill to determine how to lay the brick patio in my back yard this past Spring.

  • Practice 1 - Line GF is tangent to point E. What is EF?
  • Practice 2 - Your will use the Pythagorean Theorem to find missing sides across all of these problems.
  • Practice 3 - This is all about plugging it in to find what is missing or needs to be found.

Math Skill Quizzes

These are some unique problem types that you should see on an assessment or two.

  • Quiz 1 - You pretty much end most of these problems by taking the square root of both sides.
  • Quiz 2 - Make sure to point out where this starts and ends.
  • Quiz 3 - This will help you decide on the right values, pretty quickly.