EngageNY
Analytic Proofs of Theorems Previously Proved by Synthetic Means
Prove theorems through an analysis. Learners find the midpoint of each side of a triangle, draw the medians, and find the centroid. They then examine the location of the centroid on each median discovering there is a 1:2 relationship....
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...
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...
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
Pythagorean Theorem Proof
Tenth graders investigate the Pythagorean Theorem. Then they type up a formal paragraph proof of a proof of their choice.
Curated OER
Mathematics
Twelfth graders explore a variation of proof. In this geometry lesson, 12th graders apply their knowledge of proof to different scenario. They use 3 different tiers to advance through the lesson.
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...
Illustrative Mathematics
Joining Two Midpoints of Sides of a Triangle
Without ever using the actual term, this exercise has the learner develop the key properties of the midsegment of a triangle. This task leads the class to discover a proof of similar triangles using the properties of parallel lines cut...
EngageNY
Looking More Carefully at Parallel Lines
Can you prove it? Making assumptions in geometry is commonplace. This resource requires mathematicians to prove the parallel line postulate through constructions. Learners construct parallel lines with a 180-degree rotation and then...
Curated OER
History / Introduction of Pythagorean Theorem
Learners explore Pythagoras and the history behind his theorem. They work together to solve a proof that is embedded in the instructional activity.
Curated OER
Central Valley Math Project
Middle schoolers study the Pythagorean Theorem. They describe what it means to square a number. Pupilsuse the Pythagorean Theorem to prove the sides of given triangles, and use geometric pieces of paper to create a right triangle and...
Curated OER
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
Babylonian Mathematics 2
Students research Babylonian mathematics. They calculate simple surd numbers. Students find the fractional form of rational numbers expressed as decimals. They work with numbers in base 60.
EngageNY
Arcs and Chords
You've investigated relationships between chords, radii, and diameters—now it's time for arcs. Learners investigate relationships between arcs and chords. Learners then prove that congruent chords have congruent arcs, congruent arcs have...
Curated OER
Investigation-Reasoning and Proof
Third graders determine the outcome of each of the following situations and justify their findings: even number + even number = ?, even number + odd number = ?, odd number + odd number = ?, and odd number + even number = ?.
Curated OER
Using Properties Homework
In this geometry worksheet, 10th graders determine the property of the real number system that justifies each given statement and complete a two column proof in which they justifying the steps for solving an equation. The one page...
Curated OER
Getting It Right!
Students construct right triangles, measuring the sides and recording the measurements in spreadsheets. They analyze their measurements for patterns and research the Internet for information on Pythagoras.
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 information about...
Curated OER
Exercising With the Mathematical Induction Principle
In this math worksheet, students apply the Mathematical Induction Principle. Then they find patterns for the sums. They also read the subsequent proofs for the Induction Principle.
Curated OER
Real Life Challenge
In this consumer mathematics instructional activity, students use the newspaper to complete the sheet and figure out their budget for the next six months. They include parenting challenges and a new baby in their budget factors.
EngageNY
The Converse of the Pythagorean Theorem
Is it a right triangle or not? Introduce scholars to the converse of the Pythagorean Theorem with a lesson that also provides a proof by contradiction of the converse. Pupils use the converse to determine whether triangles with given...
EngageNY
Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
EngageNY
Congruence Criteria for Triangles—AAS and HL
How can you prove it? Guide classes through an exploration of two possible triangle congruence criteria: AAS and HL. Learners connect this criteria to those previous learned and also explore criteria that does not work. The lesson...