CK-12 Foundation's Geometry FlexBook is a clear presentation of the essentials of geometry for the high school student. Topics include: Proof, Congruent Triangles, Quadrilaterals, Similarity, Perimeter & Area, Volume, and Transformations.

Students learn why any two triangles that satisfy the AAS/HL congruence criteria must be congruent.

Students will study transformations and the role transformations play in defining congruence. The need for clear use of language is emphasized through vocabulary, the process of writing steps to perform constructions, and ultimately as part of the proof-writing process.

This student interactive, from Illuminations, allows students to explore the conditions that guarantee uniqueness of a triangle, quadrilateral, or pentagon regardless of location or orientation. Each set of conditions results in a new congruence theorem.

Texas Instruments activity that has students determine if triangles are congruent based on angles and sides.

The purpose of this task is to establish ASA, SAS and SSS as sufficient criteria for claiming that two triangles are congruent and to show how the rigid-motion transformations, along with the given congruence criteria about the two triangles, allows us to prove that the two triangles are congruent. As students work on such proofs they often overlook or reveal misconceptions about how to use the given congruence criteria in their work. Consequently, they might create a sequence of transformations that they claim carries one triangle onto the other, similar to the work they did in the previous task Can You Get There From Here, but in doing so they often assume the triangles are congruent, rather than proving them to be congruent. Therefore, the purpose of this task is less about students creating their own arguments, and more about considering the details of how such arguments can be made. Students begin by analyzing a couple of different arguments about ASA criteria for congruent triangles—one that harbors some misconceptions and one that is more explicit about the details. Then they explore other criteria for congruent triangles, such as SSS and SAS, and begin to formulate their own arguments about how they might justify such criteria using transformations.

The purpose of this task is to provide students with practice in identifying the criteria they might use—ASA, SAS or SSS—to determine if two triangles embedded in another geometric figure are congruent, and then to use those congruent triangles to make other observations about the geometric figures based on the concept that corresponding parts of congruent triangles are congruent. A secondary purpose of this task is to allow students to continue to examine what it means to make an argument based on the definitions of transformations, as well as based on properties of congruent triangles. The focus should be on using congruent triangles and transformations to identify other things that can be said about a geometric figure, rather than on the specific properties of triangles or quadrilaterals that are being observed. These observations will be more formally proved in Secondary II. The observations in this task also provide support for the geometric constructions that are explored in the next task.

This video uses the SSS, ASA, SAS, and AAS postulates to find congruent triangles.

This lesson unit is intended to help teachers assess how well students can: Understand the concepts of length and area; use the concept of area in proving why two areas are or are not equal; and construct their own examples and counterexamples to help justify or refute conjectures.

Students learn to construct an equilateral triangle.
Students communicate mathematic ideas effectively and efficiently.

Students learn why any two triangles that satisfy the SAS congruence criterion must be congruent.

Students learn why any two triangles that satisfy the ASA or SSS congruence criteria must be congruent.

Students complete proofs requiring a synthesis of the skills learned in the last four lessons.

Students complete proofs requiring a synthesis of the skills learned in the last four lessons.

I remixed the original unit by pulling out and using the notes and removing all unit numbers. I loved the notes!

This unit covers the key aspects to prove triangles are congruent. Students will learn the five triangle congruence postulates to show triangles are congruent which are SSS, SAS, ASA, AAS and HL. Additionally the students will learn about CPCTC and how it is used in showing parts of triangles are congruent. Finally the students will learn different properties of equilateral and isosceles triangles that they will be able to apply to solve different problems.