Geometry · Topic guide
Congruence — Geometry
Use precise geometric language, transformations, and congruence criteria to reason about figures and make a case for their properties.
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What you’ll learn
- Define and classify angles.
- Define circles geometrically.
- Define congruence through rigid motion.
- Select appropriate congruence criterion.
Explore the skills
Choose an idea below to read a worked example and try one question.
- Define and classify anglesDefine and classify angles.
- Define circles geometricallyDefine circles geometrically.
- Define congruence through rigid motionDefine congruence through rigid motion.
- Select appropriate congruence criterionSelect appropriate congruence criterion.
- Construct angle bisectorsConstruct angle bisectors.
- Construct parallel linesConstruct parallel lines.
- Construct perpendicular bisectorsConstruct perpendicular bisectors.
- Prove properties of isosceles trianglesProve properties of isosceles triangles.
- Prove parallelogram propertiesProve parallelogram properties.
- Prove angle relationships with parallel linesProve angle relationships with parallel lines.
- Define parallel and perpendicular linesDefine parallel and perpendicular lines.
- Use precise point/line/plane terminologyUse precise point/line/plane terminology.
- Perform and describe reflectionsPerform and describe reflections.
- Identify reflection symmetryIdentify reflection symmetry.
- Perform and describe rotationsPerform and describe rotations.
- Identify rotational symmetryIdentify rotational symmetry.
- Define segments and raysDefine segments and rays.
- Represent transformations as functionsRepresent transformations as functions.
- Construct transformation sequencesConstruct transformation sequences.
- Perform and describe translationsPerform and describe translations.
- Use ASAUse ASA.
- Use SASUse SAS.
- Use SSSUse SSS.
- Prove triangle angle sumProve triangle angle sum.
- Prove vertical-angle theoremProve vertical-angle theorem.