CCSS.Math.Content.HSG-CO.B.8
The Standard
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use translations, rotations, and reflections to place one triangle on another. They explain why SSS, SAS, or ASA forces every corresponding part to coincide.
What Mastery Looks Like
- Given two triangles, students can describe a sequence of rigid motions that makes them coincide. They can explain why the given parts leave no freedom to form a different triangle.
Common Misconceptions
- Students may think rigid motions can change side lengths or angle measures. They often treat AAA as congruence, overlook the two possible triangles in SSA, or match corresponding vertices incorrectly.
How to Assess It
- Exit ticket: Given AB = DE, AC = DF, and angle A = angle D, explain how rigid motions can map triangle ABC onto triangle DEF.
Lesson moves
Ways to Teach It
Trace two congruent triangles on transparencies, then slide, turn, or flip one tracing until corresponding sides and angles overlap.
Ask students to write why SAS fixes one triangle, while SSA can produce two different triangles.
Sort cards showing side and angle information into SSS, SAS, ASA, insufficient, or similarity only, then defend each choice.
Give students a roof-truss diagram and ask whether three measured parts prove a replacement triangular section will fit exactly.
Learning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSG-CO.B.6
Students must use rigid motions and the congruence definition before deriving why ASA, SAS, and SSS guarantee triangle congruence.
- CCSS.Math.Content.HSG-CO.B.7
Knowing congruence as rigid-motion matching of corresponding sides and angles supports proving why fewer triangle measurements guarantee congruence.
- CCSS.Math.Content.HSG-CO.A.4
Triangle congruence proofs require knowing how rotations, reflections, and translations move figures while preserving lengths and angles.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSG-SRT.B.5
Knowing why ASA, SAS, and SSS prove congruence supports choosing and justifying triangle criteria in later proofs and problems.
- CCSS.Math.Content.HSG-CO.C.11
Triangle congruence criteria justify many parallelogram proofs, such as using diagonals to show opposite sides or angles are congruent.
- CCSS.Math.Content.HSG-CO.C.10
Understanding why ASA, SAS, and SSS work supports using congruent triangles as evidence in proofs of triangle theorems.
Keep exploring
Related Standards
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.