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...
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THE MEAN INDEX CARD
Learners cut an index card to create three similar right triangles and explore the congruencies and proportions that exist. They investigate the properties of lines and concepts of congruency, similarity, tangency and symmetry of...
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Circles
In this circles worksheet, 10th graders solve and complete 13 various types of problems. First, they solve each set of triangles for the given variable. Then, students name a radius, a diameter, a tangent, a secant, a point of tangency,...
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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...
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Arc and Angles Formed by Secants and Tangents
In this calculus worksheet, students solve problems by finding the line of tangency and measure of the arcs and angles form by a secant line. There are 9 questions.
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Relationship between tangent, secant side length
In this calculus worksheet, students calculate the relationship between a line of tangency and a secant side length. They are given the formulas to solve their problems. There are 9 problems.
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Circles
Tenth graders explore and define the radius and diameter of a circle. For this geometry lesson, 10th graders calculate the circumference and area of a circle using real world objects and shapes. They discuss chords and lines tangent to a...
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Intro to Derivatives
In this calculus worksheet, students find the line tangent to a curve using the derivative. They graph the slope and identify the line of tangency. There are 6 questions.
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Tangents to a Circle
Students construct tangent lines. In this geometry lesson, students identify the point of tangency, secant and tangent lines. They graph the lines on the Ti and make observations.
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Linear Approximation
Pupils practice examining the tangent to a function to estimate the value of the function near the point of tangency. They view errors associated with those approximations, determine overestimates and find intervals that guarantee a...
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Math: Tangents
Students discover how to recognize tangents and how to use their properties. They investigate and use the properties of angles, arcs, chords, tangents, and secants. Students use two tangents and the properties of similar triangles to...
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...
NASA
Communications and the Lunar Outpost
Can you hear me now? Groups use given information about communication on the moon to determine the maximum distance an astronaut can travel and stay in communication. Using the calculations, they determine what lunar features they can...
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Punch Patterns
Fifth graders duplicate patterns, guess pattern results and identify the symmetries created. They are given an instructional handout, 5th graders replicate the patterns demonstrated by folding the paper and punching the appropriate...
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Triangle Inequality
Students discover that the sum of the lengths of any two sides of a triangle must be greater than the third side. They are shown how a triangle is formed using three strips such as that the triangle is seen inside the strips.
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Shadow Casting
Eighth graders use a meter stick that is placed on a horizontal surface and an object is moved along it so that the shadow length can be measured at different distances from the light source. They solve real-world problems involving...
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Geometry Review
In this geometry review worksheet, 10th graders solve and complete 33 different problems that include identifying various geometric figures and parts of a circle. First, they find the radius of each circle given its diameter. Then,...
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Circles
In this circles worksheet, 10th graders solve and complete 20 different problems related to various circles. First, they find the radius and diameter of a circle with a given circumference. Then, students determine the measure of each...
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Chapter 8: Circles
In this circles worksheet, high schoolers define and sketch 20 terms about circles. Students sketch radii, chords, diameters, secants, concentric circles, etc.
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What are Fractals?
Middle and high schoolers identify and analyze fractals and research information using the Internet to locate information about them. They look at fractals in relation to nature and other real world situations. Pupils create several...
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Tangent Properties
High schoolers 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. High schoolers use that...
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Understanding Fundamental Trigonometric Identities
Students are introduced to the basic trigonometric identities. Using a diagram, they discover why the parts of the unit circle as named as they are and use equations to finalize the Pythagorean trigonometric identities. They also review...
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Slope Right Up
Middle schoolers use triangles to find the length and slope of each side. After connecting the vertices, they add points based on their specific instructions. They use the Pythagorean Theorem to complete a worksheet to end the lesson.
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Let the Matrix Do It
Pupils create a matrix of the vertices of a triangle and produce new matrices that dilate, translate, rotate, and reflect the original triangle. After multiplying each matrix by a new scale factor, they graph the new matrix and describe...