EngageNY
Experiments with Inscribed Angles
Right angles, acute angles, obtuse angles, central angles, inscribed angles: how many types of angles are there? Learners first investigate definitions of inscribed angles, central angles, and intercepted arcs. The majority of the...
EngageNY
Inscribed Angle Theorem and Its Applications
Inscribed angles are central to the lesson. Young mathematicians build upon concepts learned in the previous lesson and formalize the Inscribed Angle Theorem relating inscribed and central angles. The lesson then guides learners to prove...
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 lesson then...
Curated OER
Cabri Jr. Inscribed Angles
Young scholars construct inscribed angles using Cabri Jr. They draw a circle on their graphing calculator, then construct an inscribed angle and measure its angle measures. Learners drag the inscribed angle around the circle. They make...
Mathematics Assessment Project
Inscribing and Circumscribing Right Triangles
High schoolers attempt an assessment task requiring them to find the radii of inscribed and circumscribed circles of a right triangle with given dimensions. They then evaluate provided sample responses to consider how to improve...
Texas Instraments
Angles in Circles
Teach your learners how to investigate the relationship between a central angle and an inscribed angle which subtend the same arc of a circle. The dynamic nature of Cabri Jr. provides opportunity for conjecture and verification.
Curated OER
Inscribed Angles
Students calculate the inscribed angle of a triangle. In this geometry lesson, students identify the angle created by intersection of a triangle and a circle. They see the relationship between the arc and the angle.
Mathematics Vision Project
Circles: A Geometric Perspective
Circles are the foundation of many geometric concepts and extensions - a point that is thoroughly driven home in this extensive unit. Fundamental properties of circles are investigated (including sector area, angle measure, and...
Curated OER
Circles and Angles
Students identify tangents, chords and secants. In this geometry lesson, students graph circles and identify angles created by secant lines, tangent lines and chords.
Radford University
Where Should We Sit?
Where's the best seat in the house? Given a diagram of a movie theater, pupils determine the best seats based on the viewing angle. They use inscribed angles to justify their choices.
Curated OER
Inscribing a Hexagon in a Circle
This activity is a follow-on activity to inscribing a square in a circle. The overall problem is more complex. It deals with geometric constructions, properties of triangles, and regular hexagons. The final part of the activity...
Curated OER
Inscribing a Circle in a Triangle
Pupils investigate inscribing a circle in a triangle. They use Cabri Jr. to draw a triangle, locate the incenter, and use the distance from the incenter to a side of the triangle to inscribe a circle. The dynamic nature of the geometry...
Curated OER
Triangles Inscribed in a Circle
Are you tired of answers without understanding? Learners can give a correct response, but do they really understand the concept? Have young mathematicians think deeper about linear functions, angles, and formulas in algebra....
Curated OER
Angles and Arcs
Students identify the relationship between angles and arcs. In this geometry lesson plan, students rotate and move the circle around to create different arcs on the TI-Navigator. They differentiate between major and minor arcs.
Curated OER
Inscribed Right Triangles
Young scholars calculate the measurements of the inscribed angles of a triangle. In this geometry lesson, students relate the hypotenuse of a right triangle and the diameter of a circle to each other. They calculate the diameter of a...
EngageNY
Cyclic Quadrilaterals
What does it mean for a quadrilateral to be cyclic? Mathematicians first learn what it means for a quadrilateral to be cyclic. They then investigate angle measures and area in such a quadrilateral.
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...
Curated OER
Investigating the properties of a circle
Students use wax paper to look at different properties of circles such as chords, tangent lines, inscribed angles, and inscribed angles in a semi-circle, as well as finding the center of the circle, and use GSP to investigate cyclic...
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
Circle Packing
Students identify different parts and properties of circles. In this geometry lesson, students identify the radius, diameter, semicircle and inscribed angle of a circle. They identify the tangent lines to a circle.
Curated OER
Circle Conjectures
Learners are given diagrams and are asked to make a conjecture. In this geometry lesson, students make conjectures of circles. They complete a lab activity to reinforce making conjectures. The first activity addresses a common core...
Curated OER
Properties of Arcs, Lengths and Chords
Students differentiate between the different properties of arcs, arc lengths, chords, and chord lengths. In this circles lesson, students calculate the arc length of a given circle, and find the measure of the inscribed angles of a...
Curated OER
Solving Intercepted Arcs
Students investigate circles and its arcs. In this geometry instructional activity, students identify the relationship between an circle and its intercepted arcs. THey identify the central and inscribed angles.
Curated OER
Inscribed Quadrilaterals and Parallelograms
Students differentiate between inscribed quadrilaterals and parallelograms. In this geometry lesson, students identify the shaped of the polygons when it is inscribed inside of a circle. They calculate the missing angles of the inscribed...