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Lesson Plan
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Illustrative Mathematics

Right Triangles Inscribed in Circles I

For Teachers 9th - 10th Standards
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...
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Activity
Illustrative Mathematics

Tangent to a Circle From a Point

For Teachers 9th - 10th Standards
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 information about...
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Instructional Video0:53
Corbett Maths

Angles in the Same Segment – Proof

For Students 8th - 12th Standards
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...
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Assessment
Inside Mathematics

Circles in Triangles

For Teachers 9th - 12th Standards
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...
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Lesson Plan
1
1
Illustrative Mathematics

Right Triangles Inscribed in Circles II

For Teachers 9th - 10th Standards
So many times the characteristics of triangles are presented as a vocabulary-type of lesson, but in this activity they are key to unraveling a proof. A unique attack on proving that an inscribed angle that subtends a diameter must be a...
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Lesson Plan
Virginia Department of Education

Circles in the Coordinate Plane

For Teachers 9th - 11th Standards
Make the connection between the distance formula and the equation of a circle. The teacher presents a instructional activity on how to use the distance formula to derive the equation of the circle. Pupils transform circles on the...
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Lesson Plan
EngageNY

Unknown Angle Problems with Inscribed Angles in Circles

For Teachers 9th - 10th Standards
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...
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Unit Plan
Mathematics Vision Project

Circles: A Geometric Perspective

For Teachers 10th - 12th Standards
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...
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Unit Plan
Mathematics Vision Project

Module 2: Congruence, Construction and Proof

For Teachers 9th - 12th Standards
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...
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Worksheet
Curated OER

Circle Proofs

For Students 10th
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...
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Worksheet
Curated OER

A Different Proof of the Law of Cosines

For Students 9th - 12th
In 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.
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Lesson Plan
EngageNY

Circles, Chords, Diameters, and Their Relationships

For Teachers 9th - 10th Standards
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...
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Lesson Plan
Curated OER

MOTION IN A CIRCLE

For Teachers 9th - 12th
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.
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Worksheet
1
1
Jesuit High School

Geometry Sample Problems

For Students 8th - 11th Standards
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...
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Lesson Plan
EngageNY

Ptolemy's Theorem

For Teachers 9th - 12th Standards
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.
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Lesson Plan
EngageNY

The Inscribed Angle Alternate – A Tangent Angle

For Teachers 9th - 12th Standards
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 newfound...
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Worksheet
Curated OER

Quiz: Direct Euclidean Proofs

For Students 10th - 12th
In this Euclidean proof learning exercise, students observe models and read given proofs. Students determine conclusions based upon the given information. This one-page learning exercise contains ten Euclidean proof problems.
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Lesson Plan
Curated OER

Discovering Math: Concepts in Geometry

For Teachers 8th - 12th
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.
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Lesson Plan
Curated OER

Play It

For Teachers 6th - 9th
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...
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Unit Plan
Mathematics Vision Project

Module 6: Congruence, Construction, and Proof

For Teachers 8th - 10th Standards
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 unit...
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Instructional Video19:21
2
2
Flipped Math

Intercepted Arcs

For Students 9th - 12th Standards
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...
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Handout
2
2
Curated OER

Trigonometry Review Sheet

For Students 9th - 12th Standards
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...
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Worksheet
Curated OER

Indirect Euclidean Proofs

For Students 10th
In this Euclidean proofs worksheet, 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...
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Worksheet
Curated OER

Indirect Euclidean Proofs

For Students 7th - 8th
In 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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