Curated OER
Who Let the Dogs Out?
Students calculate the perimeter and area of polygons. In this geometry instructional activity, students apply formulas of perimeter to solve geometric problems. They calculate the area of a dog fence and create ways to keep the dog in...
Curated OER
Coordinate Graphing
Students practice basic coordinate graphing and plotting points on the coordinate axis. In this geometry lesson, students are introduced to ordered pairs, and the x and y axis.
Curated OER
Origami Cube
Students compare two lengths using the area of a square. In this geometry lesson plan, students solve problems using ratio and proportion of the two shapes. They solve equations by taking the square root of both sides.
Curated OER
Ratio
Students calculate the ratio and apply it to construction. In this geometry instructional activity, students convert between different units and use decimals and fractions interchangeable. They find the fraction of a given amount...
Curated OER
Measuring Heights With Triangles
Young scholars identify the different properties of triangles. In this geometry instructional activity, students differentiate between congruent and similar triangles. They use mathematical reasoning to solve word problems.
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,...
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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...
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Construct an Equilateral Triangle (part 1)
Drawing circles isn't the only thing compasses are good for. In this first installment of a 36-part series, high schoolers learn how to draw equilateral triangles by investigating real-world situations, such as finding the location of a...
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Unknown Angle Proofs—Proofs with Constructions
Provide your emerging mathematicians with the tools to learn as they incorporate auxiliary lines to solve unknown angle proofs in this continuing segment. They decipher information from a diagram to uncover the missing pieces and...
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Special Relationships Within Right Triangles—Dividing into Two Similar Sub-Triangles
Why are right triangles so special? Pupils begin their study of right triangles by examining similar right triangles. Verifying through proofs, scholars recognize the three similar right triangles formed by drawing the altitude. Once...
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The Definition of Sine, Cosine, and Tangent
Introduce your classes to a new world of mathematics. Pupils learn to call trigonometric ratios by their given names: sine, cosine, and tangent. They find ratios and use known ratios to discover missing sides of similar...
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Trigonometry and the Pythagorean Theorem
Ancient Egyptians sure knew their trigonometry! Pupils learn how the pyramid architects applied right triangle trigonometry. When comparing the Pythagorean theorem to the trigonometric ratios, they learn an important connection that...
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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.
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Triangle Congruency Proofs (part 2)
Looking to challenge your young scholars that have mastered basic triangle congruence proofs? A collection of proofs employ previously learned definitions, theorems, and properties. Pupils draw on their past experiences with proofs...
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What Is Area?
What if I can no longer justify area by counting squares? Lead a class discussion to find the area of a rectangular region with irrational side lengths. The class continues on with the idea of lower approximations and...
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Motion Along a Line – Search Robots Again
We can mathematically model the path of a robot. Learners use parametric equations to find the location of a robot at a given time. They compare the paths of multiple robots looking for parallel and perpendicular relationships and...
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Comparing the Ratio Method with the Parallel Method
Can you prove it? Lead your class through the development of the Side Splitter Theorem through proofs. Individuals connect the ratio and parallel method of dilation through an exploration of two proofs. After completing the proofs,...
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Properties of Similarity Transformations
You can explain it, but can you do it? After learners view a sequence of transformations, the next logical step is creating the transformation. Challenge your classes to construct a composition of transformations and verify the...
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Similarity and the Angle Bisector Theorem
Identifying and verifying reproducible patterns in mathematics is an essential skill. Mathematicians identify the relationship of sides when an angle is bisected in a triangle. Once the pupils determine the relationship, they prove it to...
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Using Trigonometry to Determine Area
What do you do when you don't think you have enough information? You look for another way to do the problem! Pupils combine what they know about finding the area of a triangle and trigonometry to determine triangle area when they don't...
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Properties of Area
What properties does area possess? Solidify the area properties that pupils learned in previous years. Groups investigate the five properties using four problems, which then provide the basis for a class discussion.
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The Angle Measure of an Arc
How do you find the measure of an arc? Learners first review relationships between central and inscribed angles. They then investigate the relationship between these angles and their intercepted arcs to extend the Inscribed Angle Theorem...
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Equations for Tangent Lines to Circles
Don't go off on a tangent while writing equations of tangent lines! Scholars determine the equations for tangent lines to circles. They attempt both concrete and abstract examples, such as a tangent line to the unit circle through...
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Copy and Bisect an Angle
More constructions! In this third installment of a 36-part series, learners watch a YouTube video on creating door trim to see how to bisect an angle. They then investigate how to copy an angle by ordering a given list of steps.