Alabama Learning Exchange
Triangle Congruence with Rigid Motion
Combine transformations and triangle congruence in a single lesson. Scholars learn to view congruent triangles as a rigid transformation. Using triangle congruence criteria, learners identify congruent triangles and the rigid...
Curated OER
Triangle Congruence with Coordinate
Two triangles are displayed on a coordinate plane. Youngsters apply a reflection and a translation to demonstrate their congruence. This exercise makes a terrific tool for teaching these concepts, or a way to assess learning.
EngageNY
Triangle Congruency Proofs (part 1)
Can they put it all together? Ninth graders apply what they know about proofs and triangle congruence to complete these proofs. These proofs go beyond the basic triangle congruence proofs and use various properties, theorems, and...
EngageNY
Triangle Congruency Proofs (part 2)
Looking to challenge your students that have mastered basic triangle congruence proofs? A collection of proofs employ previously learned definitions, theorems, and properties. Pupils draw on their past experiences with proofs to...
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...
EngageNY
The Angle-Angle (AA) Criterion for Two Triangles to Be Similar
What do you need to prove triangles are similar? Learners answer this question through a construction exploration. Once they establish the criteria, they use the congruence and proportionality properties of similar objects to find...
Curated OER
Proving Triangles Congruent
Students examine Triangle Congruency. In this measurement comparison lesson, students use inductive, deductive and analytical thinking skills to prove triangle congruency. Students analyze and record their findings on activity worksheets.
Illustrative Mathematics
Similar Triangles
Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great...
Curated OER
Analyzing Congruence Proofs
Looking at numerous examples of triangles, each with different properties, geometers develop their understanding of congruency. They use the notation of a counter-example to disprove certain conjectures and prove geometric theorems and...
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...
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...
Illustrative Mathematics
Right Triangles Inscribed in Circles II
So many times the characteristics of triangles are presented as a vocabulary-type of activity, but in this activity they are key to unraveling a proof. A unique attack on proving that an inscribed angle that subtends a diameter must be a...
Willow Tree
Ratios and Proportions with Congruent and Similar Polygons
Investigate how similar and congruent figures compare. Learners understand congruent figures have congruent sides and angles, but similar figures only have congruent angles — their sides are proportional. After learning the...
Curated OER
Finding the Area of an Equilateral Triangle
The problem seems simple: find the area of the equilateral triangle whose sides are each length 1. In fact, this same problem is solved in 8th grade, addressing a different Common Core standard, using the formula for area of a triangle...
Curated OER
Why can't We Use SSA to Prove Triangles Congruent?
Students investigate triangles and congruences. In this geometry lesson, students differentiate between inductive and deductive reasoning. They differentiate between similar and congruent triangles.
Virginia Department of Education
Similar Triangles
Pupils work in pairs to investigate what it takes to prove that two triangles are similar. They work through various shortcuts to find which are enough to show a similarity relationship between the triangles. Small groups work with the...
West Contra Costa Unified School District
Investigating Similar Triangles
Let your use of the resource be in proportion to its usefulness. Pupils investigate similar triangles by measuring side lengths and considering given angle measures. The results of the investigation help develop generalizations about...
Virginia Department of Education
Congruent Triangles
Is this enough to show the two triangles are congruent? Small groups work through different combinations of constructing triangles from congruent parts to determine which combinations create only congruent triangles. Participants use the...
EngageNY
Definition of Congruence and Some Basic Properties
Build a definition of congruence from an understanding of rigid transformations. The lesson asks pupils to explain congruence through a series of transformations. Properties of congruence emerge as they make comparisons to these...
Curated OER
Exploring Characteristics Needed to Prove Two Trianlges Congruent
Tenth graders explore congruent triangles. In this geometry lesson, 10th graders investigate the conditions necessary to prove two triangles congruent. The lesson combines dry erase board activities and the use of technology.
Curated OER
Congruent Triangles Postulates
Students discover three lettered postulates that prove triangles congruent.
EngageNY
Base Angles of Isosceles Triangles
Build confidence in proofs by proving a known property. Pupils explore two approaches to proving base angles of isosceles triangles are congruent: transformations and SAS. They then apply their understanding of the proof to more complex...
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
More on the Angles of a Triangle
Angles and triangles: they're all connected. Uncover the connections between angles in triangles. Scholars learn how to find both exterior and interior angle measures in triangles. The lesson emphasizes the vocabulary related to these...