Tangent Lines Worksheets
In this section we look at how we can form lines that touch a circle at a single point. These lines are referred to as tangents. Understanding the unique proprieties that exist because of this relationship we can understand a stockpile about the plane they are located in. You can learn about the components of the circle and the angles that formed by the line. You can even learn about geometric figures that may reside outside of the circle. 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. 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.
Aligned Standard: High School Geometry - HSG-C.A.4
- Triangles Stuck in Circles Step-by-step Lesson - Use the circle as your guide to solve the triangle sides.
- Guided Lesson - I found some problems formats that skids usually find difficult and worked from there.
- Guided Lesson Explanation - It did a formatting outline for all of the problems.
- Practice Worksheet - This should be a long played sheet for you to practice with.
- Matching Worksheet -We are looking for all of the missing measures here.
- Tangents- Find the Value of x Worksheet Five Pack -You are basically looking for legs of triangles.
- Answer Keys - These are for all the unlocked materials above.
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.
What is So Special About Tangent Lines to Circles?
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. If we remember a circle is just a series of points that are all an equal distance from the center. A line that joins the exact center of the circle to any of its points is called the radius.
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. This line barely touches the curve of the circle. At this point of contact both the curve and tangent line are headed in the same direction. This leads us to a unique observation that will hold true for many of your future proof writing exercises. The tangent line to a circle is perpendicular to the radius at that point. This also has other implications like the slope of the tangent line and the slope of a curve or circle are the same. 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.
There is also another cool fact that you can pull from this relationship occurs when you come across a point found outside the circle that is positioned in such a way that when you extend two segments towards the circle and they form tangents to the circle, those line segments must be congruent.