Geometry Midterm Review PDF

‭ ath‬‭8Y‬‭-‬‭Honors‬‭Geometry‬‭Midterm‬‭Review‬‭by‬‭Unit‬ M ‭ his‬‭is‬‭a‬‭summary,‬‭it‬‭is‬‭NOT‬‭EVERYTHING!‬ T ‭Unit‬‭1:‬ ‭Geometry‬‭Vocabulary‬‭&‬‭Introduction‬ ‭Vocabulary‬‭words‬‭to‬‭know‬‭:‬ ‭Nets,‬‭point,‬‭line,‬‭plane,‬‭collinear,‬‭noncollinear,‬ ‭coplanar,...

‭ ath‬‭8Y‬‭-‬‭Honors‬‭Geometry‬‭Midterm‬‭Review‬‭by‬‭Unit‬ M ‭ his‬‭is‬‭a‬‭summary,‬‭it‬‭is‬‭NOT‬‭EVERYTHING!‬ T ‭Unit‬‭1:‬ ‭Geometry‬‭Vocabulary‬‭&‬‭Introduction‬ ‭Vocabulary‬‭words‬‭to‬‭know‬‭:‬ ‭Nets,‬‭point,‬‭line,‬‭plane,‬‭collinear,‬‭noncollinear,‬ ‭coplanar,‬‭segment,‬‭ray,‬‭parallel,‬‭skew,‬‭parallel‬‭planes,‬‭congruent,‬‭angles,‬‭opposite‬‭rays,‬ ‭angle‬‭bisector,‬‭complementary‬‭angles,‬‭supplementary‬‭angles,‬‭linear‬‭pair,‬‭perpendicular‬ ‭lines,‬‭perpendicular‬‭bisector,‬ ‭vertical‬‭angles‬ ‭Theorems:‬ ‭‬ ‭Segment‬‭addition‬ ‭‬ ‭Segment‬‭Subtraction‬ ‭‬ ‭Distance‬‭Formula‬ ‭‬ ‭Midpoint‬‭formula‬ ‭‬ ‭Vertical‬‭Angles‬ ‭Constructions:‬ ‭‬ ‭Copy‬‭segment‬ ‭‬ ‭Copy‬‭angle‬ ‭‬ ‭Angle‬‭bisector‬ ‭‬ ‭Perpendicular‬‭bisector‬ ‭Sample‬‭Problems:‬ ‭1.‬ ‭If‬‭ML‬‭is‬‭68‬‭units‬‭find‬‭,x,‬‭MV‬‭and‬‭VL.‬ ‭MV‬‭=‬‭3x‬‭-‬‭10,‬‭and‬‭VL‬‭=‬‭5x‬‭+40‬ ‭2.‬ ‭3.‬ ‭The‬‭coordinates‬‭of‬‭the‬‭midpoint‬‭of‬‭AB‬‭are‬‭(5,6).‬‭The‬‭coordinates‬‭of‬‭A‬‭are‬‭(1,‬‭−6).‬ ‭Find‬‭the‬‭coordinates‬‭of‬‭B.‬ ‭4.‬ ‭Two‬‭supplementary‬‭angles‬‭are‬‭in‬‭the‬‭ratio‬‭of‬‭4:5.‬‭Find‬‭the‬‭measure‬‭of‬‭each‬‭angle.‬ ‭5.‬ ‭6.‬ ‭Construct‬‭a‬‭right‬‭triangle,‬‭with‬‭the‬‭hypotenuse‬‭congruent‬‭to‬‭AB‬‭below.‬ ‭Unit‬‭2:‬‭Reasoning‬‭&‬‭Proof‬ ‭ ocabulary‬‭words‬‭to‬‭know‬‭:‬ ‭deductive‬‭reasoning,‬‭postulates,‬‭axioms,‬‭theorem‬ V ‭Theorems/Postulates:‬ ‭‬ ‭Reflexive‬ ‭‬ ‭Substitution‬ ‭‬ ‭Transitive‬ ‭‬ ‭Addition‬ ‭‬ ‭Subtraction‬ ‭‬ ‭Halves‬‭of‬‭Equal‬‭quantities‬‭are‬‭equal‬ ‭‬ ‭All‬‭right‬‭angles‬‭are‬‭congruent‬ ‭‬ ‭Supplements‬‭of‬‭the‬‭same‬‭(congruent‬‭angles)‬‭are‬‭congruent‬ ‭‬ ‭Linear‬‭pairs‬‭ar‬‭supplementary‬ ‭‬ ‭Complements‬‭of‬‭the‬‭same(congruent‬‭angles)‬‭are‬‭congruent‬ ‭‬ ‭Vertical‬‭Angles‬‭are‬‭congruent‬ ‭‬ ‭Constructions:‬ ‭Sample‬‭Problems:‬ ‭Unit‬‭3:‬ ‭Parallel‬‭&‬‭Perpendicular‬‭Lines‬ ‭Vocabulary:‬ ‭transversal,‬‭alternate‬‭interior‬‭angles,‬‭alternate‬‭exterior‬‭angles,‬ ‭corresponding‬‭sides,‬‭same‬‭side‬‭interior‬‭angles,‬‭same‬‭side‬‭exterior‬‭angles,‬‭auxiliary‬‭line,‬ ‭slope‬ ‭Theorems‬‭&‬‭Postulates:‬ ⇔ ‭‬ ‭Alternate‬‭interior‬‭are‬‭congruent‬‭ ‬‭||‬‭lines‬ ⇔ ‭‬ ‭Alternate‬‭exterior‬‭angles‬‭are‬‭congruent‬‭ ‬‭||‬‭lines‬  ‭‬ ⇔ ‭ orresponding‬‭angles‬‭are‬‭congruent‬‭ ‬‭||‬‭lines‬ C ‭‬ ⇔ ‭Same‬‭side‬‭interior‬‭angles‬‭are‬‭supplementary‬‭ ‬‭||‬‭lines‬ ‭‬ ⇔ ‭Same‬‭side‬‭exterior‬‭angles‬‭are‬‭supplementary‬‭ ‬‭||‬‭lines‬ ‭‬ ‭In‬‭a‬‭plane‬‭two‬‭lines‬‭||‬‭to‬‭the‬‭same‬‭line‬‭are‬‭||‬ ‭‬ ‭If‬‭two‬‭coplanar‬‭lines‬‭are‬‭perpendicular‬‭to‬‭the‬‭same‬‭line,‬‭they‬‭are‬‭||.‬ ‭‬ ‭If‬‭two‬‭lines‬‭are‬‭||‬‭they‬‭have‬‭the‬‭same‬‭slope.‬ ‭‬ ‭If‬‭two‬‭lines‬‭are‬‭vertical‬‭on‬‭a‬‭coordinate‬‭plane‬‭they‬‭are‬‭||.‬ ‭‬ ‭If‬‭two‬‭lines‬‭are‬‭perpendicular‬‭then‬‭the‬‭product‬‭of‬‭their‬‭slopes‬‭is‬‭-1.‬ ‭‬ ‭A‬‭horizontal‬‭line‬‭and‬‭a‬‭vertical‬‭line‬‭on‬‭a‬‭coordinate‬‭plane‬‭are‬‭perpendicular.‬ ‭Constructions:‬ ‭‬ ‭Parallel‬ ‭‬ ‭Parallel‬‭through‬‭a‬‭point‬ ‭‬ ‭Perpendicular‬ ‭‬ ‭Perpendicular‬‭to‬‭a‬‭point‬‭on‬‭and‬‭off‬‭the‬‭line‬ ‭Sample‬‭Problems:‬ ‭11.‬ ‭12.‬ ‭Unit‬‭4‬‭Congruent‬‭Triangles:‬ ‭Vocabulary:‬‭scalene,‬‭isosceles,‬‭equilateral,‬‭acute,‬‭right,‬‭obtuse,‬‭interior,‬‭exterior,‬ ‭remote‬‭interior‬‭angle,‬‭included‬‭side,‬‭included‬‭angle,‬‭vertex‬‭angle,‬‭base‬‭angle,‬‭legs,‬ ‭Theorems:‬ ‭‬ ‭Sum‬‭of‬‭the‬‭interior‬‭angles‬‭of‬‭a‬‭triangle‬‭is‬‭180.‬ ‭‬ ‭The‬‭measure‬‭of‬‭an‬‭exterior‬‭angle‬‭of‬‭a‬‭triangle‬‭is‬‭the‬‭sum‬‭of‬‭the‬ ‭remote‬‭interior‬‭angles.‬ ‭‬ ‭If‬‭two‬‭angles‬‭of‬‭a‬‭triangle‬‭are‬‭congruent‬‭to‬ ‭two‬‭angles‬‭of‬‭another‬ ‭triangle,‬‭the‬‭third‬‭angles‬‭are‬‭congruent.‬ ‭‬ ‭SSS,‬‭SAS,‬‭ASA,‬‭AAS,‬‭HL‬ ‭‬ ‭In‬‭a‬‭triangle‬‭sides‬‭opposite‬‭congruent‬‭angles‬‭are‬‭congruent.‬ ‭‬ ‭In‬‭a‬‭triangle,‬‭angles‬‭opposite‬‭congruent‬‭sides‬‭are‬‭congruent.‬ ‭Sample‬‭Problems:‬ ‭Unit‬‭5:‬‭Relationships‬‭in‬‭Triangles‬ ‭Vocabulary:‬‭concurrent,‬‭point‬‭of‬‭concurrency,‬‭circumscribed,‬‭inscribed,‬ ‭circumcenter,‬‭incenter,‬‭median,‬‭centroid,‬‭altitude,‬‭orthocenter,‬‭partition,‬ ‭directed‬‭segment,‬‭indirect‬‭proof‬ ‭Theorems:‬ ‭‬ ‭The‬‭perpendicular‬‭bisectors‬‭of‬‭the‬‭sides‬‭of‬‭the‬‭triangle‬‭are‬ ‭concurrent‬‭at‬‭a‬‭point‬‭equidistant‬‭from‬‭the‬‭vertices.‬ ‭(Circumcenter)‬ ‭‬ ‭The‬‭bisectors‬‭of‬‭the‬‭angles‬‭of‬‭a‬‭triangle‬‭are‬‭concurrent‬‭at‬‭a‬ ‭point‬‭equidistant‬‭from‬‭the‬‭sides‬‭of‬‭the‬‭triangle.‬‭(Incenter)‬  ‭‬ T ‭ he‬‭point‬‭of‬‭concurrency‬‭of‬‭the‬‭median‬‭of‬‭a‬‭triangle‬‭is‬‭the‬ ‭centroid‬‭which‬‭is‬‭⅔‬‭the‬‭distance‬‭from‬‭the‬‭vertex‬‭on‬‭the‬‭median.‬ ‭‬ ‭The‬‭point‬‭of‬‭concurrency‬‭of‬‭the‬‭altitudes‬‭of‬‭the‬‭triangle‬‭is‬‭the‬ ‭orthocenter.‬ ‭‬ ‭Theorem:‬‭an‬‭exterior‬‭angle‬‭of‬‭a‬‭∆‬‭is‬‭greater‬‭than‬‭either‬‭of‬‭its‬ ‭non-adjacent‬‭(remote)‬‭interior‬‭angles.‬ ‭‬ ‭In‬‭a‬‭triangle,‬‭the‬‭longest‬‭side‬‭is‬‭opposite‬‭the‬‭largest‬‭angle,‬‭the‬ ‭smallest‬‭side‬‭opposite‬‭the‬‭smallest‬‭angle.‬ ‭‬ ‭In‬‭a‬‭triangle‬‭the‬‭sum‬‭of‬‭two‬‭sides‬‭is‬‭greater‬‭than‬‭the‬‭length‬‭of‬ ‭the‬‭third‬‭side.‬ ‭‬ ‭Constructions:‬ ‭‬ ‭Perpendicular‬‭bisector‬ ‭‬ ‭Circumcenter‬ ‭‬ ‭Incenter‬ ‭‬ ‭Angle‬‭bisector‬ ‭‬ ‭Median‬ ‭‬ ‭Centroid‬ ‭‬ ‭Altitude‬ ‭‬ ‭Orthocenter‬ ‭‬ R ‭ eview‬‭the‬‭partition‬‭process‬ ‭‬ ‭Review‬‭Indirect‬‭Proofs‬ ‭Sample‬‭Problems:‬  ‭7‬ ‭8‬ ‭9.‬ ‭10‬ ‭11‬ ‭12‬ ‭Unit‬‭6‬‭Quadrilaterals:‬ ‭Vocabulary:‬‭regular‬‭polygon,‬‭quadrilateral,‬‭kite,‬‭trapezoid,‬‭parallelogram,‬ ‭rhombus,‬‭rectangle,‬‭square‬ ‭Theorems;‬ ‭‬ ‭The‬‭sum‬‭of‬‭the‬‭angles‬‭of‬‭any‬‭polygon‬‭are‬‭(n-2)‬‭180.‬ ‭‬ ‭The‬‭sum‬‭of‬‭the‬‭exterior‬‭angles‬‭of‬‭a‬‭polygon‬‭is‬‭360.‬ ‭‬ ‭Parts‬‭and‬‭extensions‬‭of‬‭parallel‬‭lines‬‭are‬‭parallel‬ ‭‬ ‭If‬‭a‬‭parallelogram‬‭has‬‭one‬‭right‬‭angle‬‭then‬‭it‬‭has‬‭4‬‭right‬‭angles.‬ ‭Properties‬‭of:‬ ‭Parallelogram:‬ ‭‬ ‭2‬‭pair‬‭of‬‭parallel‬‭sides.‬ ‭‬ ‭2‬‭pair‬‭congruent‬‭sides.‬ ‭‬ ‭Opposite‬‭angles‬‭are‬‭congruent.‬ ‭‬ ‭Diagonals‬‭bisect‬‭each‬‭other.‬ ‭‬ ‭Consecutive‬‭angles‬‭are‬‭supplementary.‬ ‭Rectangle:‬ ‭‬ ‭ALL‬‭PROPERTIES‬‭OF‬‭A‬‭PARALLELOGRAM‬ ‭‬ ‭All‬‭right‬‭angles.‬ ‭‬ ‭Diagonals‬‭are‬‭congruent.‬ ‭Rhombus:‬ ‭‬ ‭ALL‬‭PROPERTIES‬‭OF‬‭A‬‭PARALLELOGRAM‬ ‭‬ ‭All‬‭sides‬‭are‬‭congruent.‬ ‭‬ ‭Diagonals‬‭are‬‭perpendicular‬ ‭‬ ‭Diagonals‬‭bisect‬‭the‬‭angles‬ ‭Square:‬ ‭‬ ‭All‬‭properties‬‭of‬‭a‬‭rectangle.‬ ‭‬ ‭All‬‭properties‬‭of‬‭a‬‭rhombus‬ ‭Kites-‬‭it‬‭is‬‭not‬‭a‬‭parallelogram‬ ‭‬ ‭Two‬‭pairs‬‭of‬‭adjacent‬‭congruent‬‭sides.‬ ‭‬ ‭The‬‭diagonals‬‭are‬‭perpendicular.‬ ‭‬ ‭The‬‭main‬‭(longer)‬‭diagonal‬‭bisects‬‭the‬‭other.‬ ‭‬ ‭The‬‭angles‬‭between‬‭noncongruent‬‭sides‬‭are‬‭congruent.‬ ‭‬ ‭The‬‭main‬‭diagonal‬‭bisects‬‭the‬‭angles.‬ ‭Trapezoid-‬‭is‬‭not‬‭a‬‭parallelogram‬ ‭‬ ‭At‬‭least‬‭one‬‭pair‬‭of‬‭parallel‬‭sides.‬ ‭Isosceles‬‭Trapezoid-‬‭the‬‭nonparallel‬‭sides‬‭are‬‭congruent.‬ ‭‬ ‭The‬‭base‬‭angles‬‭are‬‭congruent‬‭(‬‭2‬‭pairs)‬ ‭‬ ‭The‬‭diagonals‬‭are‬‭congruent‬ ‭‬ ‭Review‬‭coordinate‬‭proofs.‬ ‭Sample‬‭Problems:‬ ‭1.‬ ‭If‬‭the‬‭sum‬‭of‬‭the‬‭interior‬‭angles‬‭of‬‭a‬‭polygon‬‭is‬‭1440°,‬‭then‬‭the‬‭polygon‬‭must‬‭be‬ ‭2.‬ ‭What‬‭is‬‭the‬‭measure‬‭of‬‭each‬‭interior‬‭angle‬‭of‬‭a‬‭regular‬‭hexagon.‬ ‭3.‬ ‭What‬‭is‬‭the‬‭measure‬‭of‬‭the‬‭largest‬‭exterior‬‭angle‬‭that‬‭any‬‭regular‬‭polygon‬‭can‬ ‭have?‬ ‭5.‬‭A‬‭quadrilateral‬‭must‬‭be‬‭a‬‭parallelogram‬‭if‬ ‭1)‬‭one‬‭pair‬‭of‬‭sides‬‭is‬‭parallel‬‭and‬‭one‬‭pair‬‭of‬‭angles‬‭is‬‭congruent‬ ‭2)‬‭one‬‭pair‬‭of‬‭sides‬‭is‬‭congruent‬‭and‬‭one‬‭pair‬‭of‬‭angles‬‭is‬‭congruent‬ ‭3)‬‭one‬‭pair‬‭of‬‭sides‬‭is‬‭both‬‭parallel‬‭and‬‭congruent‬ ‭4)‬‭the‬‭diagonals‬‭are‬‭congruent‬ ‭.‬‭If‬‭the‬‭diagonals‬‭of‬‭a‬‭quadrilateral‬‭do‬‭not‬‭bisect‬‭each‬‭other,‬‭then‬‭the‬‭quadrilateral‬‭could‬ 6 ‭be‬‭a‬‭1)‬‭rectangle‬‭2)‬‭rhombus‬‭3)‬‭square‬‭4)‬‭trapezoid‬ ‭.‬‭Which‬‭set‬‭of‬‭statements‬‭would‬‭describe‬‭a‬‭parallelogram‬‭that‬‭can‬‭always‬‭be‬‭classified‬ 9 ‭as‬‭a‬‭rhombus?‬ ‭I.‬‭Diagonals‬‭are‬‭perpendicular‬‭bisectors‬‭of‬‭each‬‭other.‬ ‭II.‬‭Diagonals‬‭bisect‬‭the‬‭angles‬‭from‬‭which‬‭they‬‭are‬‭drawn.‬ ‭III.‬‭Diagonals‬‭form‬‭four‬‭congruent‬‭isosceles‬‭right‬‭triangles.‬ ‭1)‬‭I‬‭and‬‭II‬ ‭2)‬‭I‬‭and‬‭III‬ ‭3)‬‭II‬‭and‬‭III‬ ‭4)‬‭I,‬‭II,‬‭and‬‭III‬ ‭ 0.‬ ‭A‬‭set‬‭of‬‭five‬‭quadrilaterals‬‭consists‬‭of‬‭a‬‭square,‬‭a‬‭rhombus,‬‭a‬‭rectangle,‬‭an‬ 1 ‭isosceles‬‭trapezoid,‬‭and‬‭a‬‭parallelogram.‬‭Lu‬‭selects‬‭one‬‭of‬‭these‬‭figures‬‭at‬‭random.‬ ‭What‬‭is‬‭the‬‭probability‬‭that‬‭both‬‭pairs‬‭of‬‭the‬‭figure's‬‭opposite‬‭sides‬‭are‬‭parallel?‬ ‭1)‬‭1‬ ‭2)‬‭⅘‬ ‭3)‬‭¾‬ ‭4)‬‭⅖‬