EngageNY
Congruence Criteria for Triangles—ASA and SSS
How do you know if a pair of triangles are congruent? Use the lesson to help class members become comfortable identifying the congruence criteria. They begin with an exploration of ASA and SSS criteria through transformations and...
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...
EngageNY
Tangent Segments
What's so special about tangents? Learners first explore how if a circle is tangent to both rays of an angle, then its center is on the angle bisector. They then complete a set of exercises designed to explore further properties and...
EngageNY
Thales’ Theorem
Isn't paper pushing supposed to be boring? Learners attempt a paper-pushing puzzle to develop ideas about angles inscribed on a diameter of a circle. Learners then formalize Thales' theorem and use geometric properties to develop a proof...
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...
EngageNY
Review of the Assumptions (part 2)
Is the amount of information getting overwhelming for your geometry classes? Use this strategy as a way to organize information. The resource provides a handout of information studied in relation to triangle congruence. It includes a...
Curated OER
The Truth About Triangles And Proofs
Students engage in a lesson plan that is about the classification of triangles and the mathematical proofs involved in working with them. They work on a variety of problems that are created by the teacher with the focus upon the...
Curated OER
Indirect Proof and Inequalities in One Triangle
In this geometry worksheet, 10th graders order the sides and angles of a triangle and determine the range of the third side of a triangle given the lengths of two sides. The one page worksheet contains sixteen questions. Answers are...
EngageNY
Mid-Module Assessment Task - Geometry (Module 1)
How do you prepare class members for the analytical thinking they will need in the real world? An assessment requires the higher order thinking they need to be successful. The module focuses on the concept of rigid transformations...
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...
Curated OER
Investigating AAS
Students investigate the theorems of ASA, AAS, AAA and ASA. In this geometry lesson, students discuss the theorems of triangles and how it is used to solve for missing sides or angles. They review how two angles are formed by two rays...
Curated OER
Probability and Geometry
Students practice calculating probability, see how geometry can help solve probability problems and explore platonic solids.
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...
NASA
Foam Rocket
When going for distance, does it make a difference at what angle you launch the rocket? Teams of three launch foam rockets, varying the launch angle and determining how far they flew. After conducting the series of flights three times,...
Curated OER
Special Segments in a Triangle
In this geometry worksheet, 10th graders review the vocabulary associated with the special segments of a triangle and the associated points of concurrency and solve problems in which they find the indicated missing angle or segment. The...
Alabama Learning Exchange
Triangle Area: No Height? Use the Sine
No height? No problem! Learners use their knowledge and a little help from GeoGebra to develop the Law of Sines formula. The Law of Sines helps to determine the height of triangles to calculate the area.
EngageNY
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...
Virginia Department of Education
Pythagorean Theorem
Investigate the meaning of the Pythagorean Theorem through modeling. After comparing the area of the square of each side, individuals cut triangles and squares to facilitate the comparison.
Curated OER
Why Doesn't SSA Work?
Students investigate the relationship between angles and their sides. In this geometry lesson, students prove why SSA does not work as a true angle side relationship theorem.
Curated OER
Inequalities and Triangles
Students prove and apply theorems of triangle inequality and hinge theorem. In this geometry lesson, students will discuss which triangle is bigger and why. They will use theorems, such as Exterior Angle Inequality or the Pythagorean...
EngageNY
Review of the Assumptions (part 1)
What was the property again? Tired of hearing this from your pupils? Use this table to organize properties studied and as a reference tool for individuals. Learners apply each property in the third column of the table to ensure their...
Curated OER
Pythagorean Theorem by Graphic Manipulation
There are many different ways to show a proof of the Pythagorean Theorem. Here is a nice hands-on paper cutting activity that shows a graphic representation. You can even challenge your young Pythagoreans to come up with their own...
EngageNY
Prove the Pythagorean Theorem Using Similarity
Amaze your classes with the ability to find side lengths of triangles immediately — they'll all want to know your trick! Learners use the Pythagorean Theorem and special right triangle relationships to find missing side lengths.
Curated OER
Picking Pythagoras
Learners discover that side measurement is used in determining angle classification of a triangle. By squaring sides, they predict whether triangles be right, obtuse, or acute. They prove the Pythagorean Theorem and use it to solve...