EngageNY
Unknown Angle Problems with Inscribed Angles in Circles
We know theorems about circles—now what? Class members prove a theorem, with half the class taking the case where a point is inside the circle and half the class taking the case where a point is outside the circle. The activity then...
EngageNY
Inscribed Angle Theorem and Its Applications
Inscribed angles are central to the instructional activity. Young mathematicians build upon concepts learned in the previous instructional activity and formalize the Inscribed Angle Theorem relating inscribed and central angles. The...
EngageNY
Circles, Chords, Diameters, and Their Relationships
A diameter is the longest chord possible, but that's not the only relationship between chords and diameters! Young geometry pupils construct perpendicular bisectors of chords to develop a conjecture about the relationships between chords...
EngageNY
Thales’ Theorem
Isn't paper pushing supposed to be boring? Learners attempt a paper-pushing puzzle to develop ideas about angles inscribed on a diameter of a circle. Learners then formalize Thales' theorem and use geometric properties to develop a proof...
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...
Curated OER
Worksheet 5: Property Limits and the Squeeze Theorem
In this math worksheet, learners answer 6 questions regarding given limits in a table of data, properties of limits and the Squeeze Theorem.
EngageNY
Ptolemy's Theorem
Everyone's heard of Pythagoras, but who's Ptolemy? Learners test Ptolemy's Theorem using a specific cyclic quadrilateral and a ruler in the 22nd installment of a 23-part module. They then work through a proof of the theorem.
Curated OER
Worksheet 5 - Squeeze Theorem
In this Squeeze Theorem worksheet, students compute limits, identify a graph that represents the Squeeze Theorem, and graph given functions. This two-page worksheet contains seven multi-step problems.
Futures Channel
Folding Circles
Students investigate properties of circles. In this geometry lesson plan, students differentiate between similarity and congruence as they observe polygons. They investigate properties of two and three dimensional shape.
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.
Mathematics Assessment Project
Solving Problems with Circles and Triangles
After completing a task involving examining the ratio of areas of triangles and circles in a given figure, scholars examine sample responses to identify other strategies they could use to solve the problem.
Mathematics Assessment Project
Sorting Equations of Circles 2
How much can you tell about a circle from its equation? This detailed lesson plan focuses on connecting equations and graphs of circles. Learners use equations to identify x- and y-intercepts, centers, and radii of circles. They also...
EngageNY
What Is a Trigonometric Identity?
Protect yourself from identity theft! Establishing a strong understanding of the Pythagorean identity allows learners to prove that sine^2x + cos^2x = 1. They then use the identity to find sine or cosine ratios given the other.
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,...
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...
Curated OER
Circle, Secants
Students identify the secant segment of a circle. In this geometry lesson plan, students investigate secant lines formed outside the circle. They use Cabri software to create drawings and explore circles and secants.
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...
Mathematics Assessment Project
Modeling Motion: Rolling Cups
Connect the size of a rolling cup to the size of circle it makes. Pupils view videos of cups of different sizes rolling in a circle. Using the videos and additional data, they attempt to determine a relationship between cup...
Curated OER
Investigating AAS
Students investigate the theorems of ASA, AAS, AAA and ASA. In this geometry lesson, students discuss the theorems of triangles and how it is used to solve for missing sides or angles. They review how two angles are formed by two rays...
Curated OER
Determining the Uniqueness of a Circle
Young scholars use this lesson to determine how circles are different from other shapes. In groups, they determine the accuracy of three theorems based on the uniqueness of circles. They use a software program to hypothesize about the...
Curated OER
Discovering Math: Concepts in Geometry
Middle and high schoolers explore the concept of proving the Pythagorean Theorem. They research proofs of the Pythagorean Theorem. Pupils create posters of proofs, and research Greek mathematicians.
Curated OER
Exploring Secants: Products of Segments
Students explore secants and circles. In this geometry instructional activity, students identify the properties of two and three dimensional shapes. They create arguments to prove the theorems are true.
EngageNY
Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
Curated OER
Why Doesn't SSA Work?
Students investigate the relationship between angles and their sides. For this geometry lesson, students prove why SSA does not work as a true angle side relationship theorem.