Illustrative Mathematics
Right Triangles Inscribed in Circles I
One of the basic properties of inscribed angles gets a triangle proof treatment in a short but detailed exercise. Leading directions take the learner through identifying characteristics of a circle and how they relate to angles and...
Illustrative Mathematics
Tangent to a Circle From a Point
Learners see application of construction techniques in a short but sophisticated problem. Combining the properties of inscribed triangles with tangent lines and radii makes a nice bridge between units, a way of using...
Corbett Maths
Angles in the Same Segment – Proof
If angles intercept the same arc, the angles must be the same size. The quick video talks through the proof of showing the reason two inscribed angles that intersect the same arc have the same measurement. Pupils then create their own...
Inside Mathematics
Circles in Triangles
Challenge the class with inscribed circles in triangles. The assessment task requests class members use their knowledge of circles and right triangles to prove two triangles are congruent. They go on to utilize their knowledge of...
Illustrative Mathematics
Right Triangles Inscribed in Circles II
So many times the characteristics of triangles are presented as a vocabulary-type of instructional activity, but in this activity they are key to unraveling a proof. A unique attack on proving that an inscribed angle that subtends a...
Virginia Department of Education
Circles in the Coordinate Plane
Make the connection between the distance formula and the equation of a circle. The teacher presents a lesson on how to use the distance formula to derive the equation of the circle. Pupils transform circles on the coordinate plane and...
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...
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...
Mathematics Vision Project
Module 2: Congruence, Construction and Proof
Construct yourself a winning geometry unit. A set of lessons introduces geometry scholars to constructions and proofs with compasses and straightedges. It also covers triangle congruence through transformations. This is the second of...
Curated OER
Circle Proofs
In this circle proofs worksheet, 10th graders complete 4 different problems that include circle proofs. They respond to each of the questions that deal with circle proofs. Then, students read the given information and use the circle...
Curated OER
A Different Proof of the Law of Cosines
For this proofs worksheet, students construct 1 proof of the law of cosines. Students construct a right triangle within a circle to prove the law of cosines.
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...
Curated OER
MOTION IN A CIRCLE
Students explore uniform circular motion, and the relation of its frequency of N revolutions/sec with the peripheral velocity v and with the rotation period T, and the "centripetal acceleration" of an object.
Jesuit High School
Geometry Sample Problems
I'd like to prove that this worksheet has a lot to offer. Seven problems using triangles and parallelograms practice the traditional method of a two-column proof. After the worksheet is some practice problems that show worked out...
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.
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
Quiz: Direct Euclidean Proofs
For this Euclidean proof worksheet, students observe models and read given proofs. Students determine conclusions based upon the given information. This one-page worksheet contains ten Euclidean proof problems.
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
Play It
There are a number of activities here that look at representing data in different ways. One activity, has young data analysts conduct a class survey regarding a new radio station, summarize a data set, and use central tendencies to...
Mathematics Vision Project
Module 6: Congruence, Construction, and Proof
Trace the links between a variety of math concepts in this far-reaching unit. Ideas that seem very different on the outset (like the distance formula and rigid transformations) come together in very natural and logical ways. This...
Flipped Math
Intercepted Arcs
Intercept the class's learning on circles. Pupils learn the relationship between intercepted arcs and inscribed angles. The scholars use that information to find the relationship of angles in an inscribed quadrilateral and an angle...
Curated OER
Trigonometry Review Sheet
Get the trig facts fast, and use the review sheet as a guide in the classroom. The worksheet also includes a document version if any changes are needed to the problems. The information includes a small degree/radian chart, a graph of all...
Curated OER
Indirect Euclidean Proofs
In this Euclidean proofs activity, 10th graders solve 10 different problems that include completing indirect Euclidean proofs. First, they write a statement for each of the reasons listed on the sheet of proofs. Then, students solve the...
Curated OER
Indirect Euclidean Proofs
For this indirect Euclidean proof worksheet, students write statements supporting the reasons for a given proof. This one-page worksheet contains ten problems.
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