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...
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...
Mathematics Vision Project
Geometric Figures
Logical thinking is at the forefront of this jam-packed lesson, with young mathematicians not only investigating geometric concepts but also how they "know what they know". Through each activity and worksheet, learners wrestle with...
Curated OER
Pythagoras' Theorem
Students are introduced to the Pythagoras' Theorem and its history, proofs and practice in application. Students find perimeters, areas and volume of everyday objects. Students state and explain the theory.
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Extra Practice with Proofs
In this practice with proofs worksheet, students give a reason for each step of a proof. They complete missing portions of a proof. This one-page worksheet contains three multi-step problems.
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The Pythagorean Theorem Lesson 2
Learners discuss and review examples of the Pythagorean Theorem using a GSP, Geometer's Sketchpad, activity.
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Number Theory
Learners explore the concept of number theory. They discuss an assortment of number theory topics such as prime numbers, composite numbers, GCF, modular arithmetic, and others in a lecture style discussion. Pupils view videos about these...
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.
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Euclidean Direct Proofs
Learning how to prove theorems in geometry can be challenging. This resource explains what a proof is, and the different styles for proofs. It also contains links to web-based practice problems that help guide learners though example...
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Proofs
In this geometric proof instructional activity, students compose 20 triangle congruency proofs. Students will decide if there is enough information in problems 1-6 to prove if any triangles are congruent. In problems 17 to 20, students...
Curated OER
SSS, SAS, ASA, and AAS Congruence
Students will determine if triangles are congruent and state the appropriate congruence theorem. In this geometry lesson, students will determine what information is needed to determine if a pair of triangles are congruent using ASA,...
Curated OER
Right Triangle congruence
Students will determine if two triangles are congruent and which property is used. In this lesson on right triangles, students will determine what additional information is need to make a pair of triangles congruent.
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Challenge: Skills and Applications Lesson 1.3
In this skills instructional activity, learners explain the Segment Addition Postulate, provide examples and counter examples and determine congruent line segments. This one-page instructional activity contains 11 multi-step problems.
Curated OER
Product + 1: Integers
In this integers worksheet, high schoolers solve 1 word problem using proof. Students prove their hypothesis of the result of multiplying four consecutive positive integers and adding one to the product.
Curated OER
Proof That One Equals Zero (Using Calculus)
For this proofs worksheet, learners evaluate the integral of 1 function. Students use uv-substitution to prove 0=1.
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Inequalities and Triangles
Students prove and apply theorems of triangle inequality and hinge theorem. For this geometry lesson, students will discuss which triangle is bigger and why. They will use theorems, such as Exterior Angle Inequality or the Pythagorean...
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.
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TI Workshop Presentation Guide for "Preparing for Proofs"
Pupils discover proofs using the TI in this geometry activity. They collect data from newspaper and magazines and analyze their data using the TI, relating it to proofs.
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Points, Lines and Planes
For this points, lines and planes worksheet, 10th graders solve and complete 9 various types of problems. First, they name the planes that intersect a figure shown. Then, students determine the points that are collinear and coplanar in...
Curated OER
Geometry Concepts and Applications
In this concepts and applications review worksheet, 10th graders solve and complete 40 various types of multiple choice problems. First, they write the equation of a vertical line passing through a point. Then, students find the...
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Primes and Prime Factors
In this primes and prime factors worksheet, 8th graders solve 21 different problems to include identifying each number as prime, composite, or neither prime nor composite and listing all the primes less than 200. Then they complete each...
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The Pythagorean Theorem
Young scholars create both a visual and formal proof of the Pythagorean theorem, as well as view four additional geometric demonstrations of the theorem. They construct a square and conjecture the following theorem: The sum of the areas...
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Prize Numbers
Students explore what a proof is, how and why mathematicians create them and compose essays on how reason and logic are employed in the workplace. They explore whether any three lines can make a triangle and attempt to verify Goldbach's...
Curated OER
Easy Worksheet: Congruent Segments
In this congruent segments learning exercise, students solve 6 short answer problems. Students justify steps in a proof by identifying the reason for various steps. Students justify steps of proofs using the transitive property,...