## High School Plane Geometry Through Transformations: An Exploratory Study, Volume 1 |

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ability achievement test algebraic analysis of covariance angle approach association assumed axiom set bisector called Category chapter classes completed concept conclusions congruence consider contains correspondence course defined Definition designed determine developed diagram distance distribution elements Euclidean exercises exists expected experimental feasibility figures final four given Grade Guggenheimer's half-plane high school idea important included indicated intersect introduced intuitive invariant IQ Quartiles Items knowledge lessons mapping materials Mathematics means motion noted observed one-to-one pair parallel lines performance perpendicular plane geometry population possible Postulate pre-test presenting Previous Mathematics Class problems projective proofs properties Prove questions reflection represent rotation scores segment selection sides similarity space statement Subtest summarized Table teachers teaching Theorem topics Total Test transformation geometry translations triangle unique unit variable various vectors