Georgia Department of Education
Analytic Geometry Study Guide
Are you looking for a comprehensive review that addresses the Common Core standards for geometry? This is it! Instruction and practice problems built specifically for standards are included. The material includes geometry topics from...
EngageNY
Special Lines in Triangles (part 2)
Medians, midsegments, altitudes, oh my! Pupils study the properties of the median of a triangle, initially examining a proof utilizing midsegments to determine the length ratio of a median. They then use the information to find missing...
EngageNY
Congruence Criteria for Triangles—SAS
Looking for a different approach to triangle congruence criteria? Employ transformations to determine congruent triangles. Learners list the transformations required to map one triangle to the next. They learn to identify congruence if...
Education Development Center
Sum of Rational and Irrational is Irrational
Sometimes the indirect path is best. Scholars determine whether the sum of a rational number and an irrational number is irrational. Reading a transcript of a conversation between classmates leads to an indirect proof of this concept.
Curated OER
Thesis-Proof Graphic Organizer
In this thesis-proof graphic organizer worksheet, students fill in a thesis, and the supporting and refuting evidence. They write a conclusion paragraph on the lines provided below the organizer.
Chapman University
Derivative of sin x
Direct and to the point (the slope at a point that is) describes this one-page proof of the derivative of the sin(x). The definition of a derivative using a limit is the first step in this sequential, algebraic, explanation of how the...
Curated OER
The Proof of the Century!
Students do Web research in the field of mathematics. They explore mathematical proofs and apply them to the Pythagorean theorem. They also explore the general ideas of Fermat's Last Theorem
Curated OER
Preparation and Transition to Two-Column Proofs
Students investigate proofs used to solve geometric problems. In this geometry lesson, students read about the history behind early geometry and learn how to write proofs correctly using two columns. The define terminology valuable to...
Curated OER
Proof that One Equals Zero and Zero Equals Two
In this algebra worksheet, 11th graders complete proofs that show why properties are true. There are 2 proofs given with 8 required steps.
Curated OER
Proof by Induction
Twelfth graders define and prove theorems using induction. In this calculus lesson plan, 12th graders differentiate between inductive reasoning and deductive reasoning. They review sigma notations and work proofs by induction.
Curated OER
The Pythagorean Theorem
Learners 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 of...
Curated OER
Product + 1: Integers
In this integers instructional activity, students 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
The Proof
Learners will construct simple curves on graph paper by connecting a series of points between the vertical and horizontal axes. They share their designs and explain the patterns.
Curated OER
Proofs Chapter 2: Geometry
In this geometry worksheet, students look at given pictures and prove congruent lines and angles. This three-page worksheet contains nine multi-step problems.
Curated OER
Coordinate Proofs
Students explore the concept of coordinate proofs. In this coordinate proofs lesson, students write coordinate proofs using properties of distance, slope, and midpoint. Students discuss why it is sometimes beneficial to double the...
Curated OER
Pythagorean Theorem Proof
Tenth graders investigate the Pythagorean Theorem. Then they type up a formal paragraph proof of a proof of their choice.
Mt. San Antonio Collage
Congruent Triangles Applications
Triangles are all about threes, and practicing proving postulates is a great way to get started. The first page of the learning exercise provides a brief introduction of the different properties and postulates. The remaining pages...
EngageNY
Characteristics of Parallel Lines
Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...
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
Properties of Parallelograms
Everyone knows that opposite sides of a parallelogram are congruent, but can you prove it? Challenge pupils to use triangle congruence to prove properties of quadrilaterals. Learners complete formal two-column proofs before moving on to...
Illustrative Mathematics
Equal Area Triangles on the Same Base II
A deceptively simple question setup leads to a number of attack methods and a surprisingly sophisticated solution set in this open-ended problem. Young geometers of different strengths can go about defining the solutions graphically,...
Illustrative Mathematics
Are They Similar?
Learners separate things that just appear similar from those that are actually similar. A diagram of triangles is given, and then a variety of geometric characteristics changed and the similarity of the triangles analyzed. Because the...
Mathematics Assessment Project
Cross Totals
Finally, it all adds up. Learners complete a number puzzle in which they investigate the sums of the digits one through nine in a cross pattern. They then try to determine what totals are possible and which ones are not before devising a...
Radford University
Parallel Lines Cut by a Transversal
Use the parallel lines to find your way. After first reviewing geometric constructions and the relationships between angles formed by parallel lines and a transversal, young mathematicians write proofs for theorems relating to parallel...
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