CCSS.Math.Content.HSG-SRT.B.5
The Standard
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide whether two triangles are congruent or similar using given sides and angles. They use that conclusion to find missing measures or prove relationships between parts of a figure.
What Mastery Looks Like
- Students select a valid congruence or similarity criterion from a diagram or set of facts. They justify the match between vertices, find missing measures, and use the result to prove another relationship.
Common Misconceptions
- Students may use AAA or SSA to claim triangles are congruent. They also match noncorresponding sides in proportions or assume similar triangles have equal side lengths.
How to Assess It
- Exit ticket: Triangles ABC and DEF have AB = 6, BC = 9, DE = 10, EF = 15, and angles B and E congruent. Name the similarity criterion, then find DF if AC = 12.
Lesson moves
Ways to Teach It
Build paper triangles from given side and angle measures, then overlay them to decide which congruence or similarity criterion applies.
Explain why AAA proves similarity but not congruence, using two triangles with the same angles and different side lengths.
Run a card sort matching triangle diagrams, valid criteria, proportional equations, and conclusions about missing lengths or angles.
Measure a flagpole’s shadow and a meter stick’s shadow, then use similar triangles to estimate the flagpole’s height.
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Printable HSG-SRT.B.5 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-SRT.B.5, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSG-CO.B.8
Knowing why ASA, SAS, and SSS prove congruence supports choosing and justifying triangle criteria in later proofs and problems.
- CCSS.Math.Content.HSG-SRT.A.3
Establishing AA similarity supports later use of triangle similarity criteria to solve problems and justify figure relationships.
- CCSS.Math.Content.HSG-CO.C.10
Proving triangle theorems develops the angle, side, and auxiliary-line reasoning often used with congruence and similarity criteria.
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