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Geometry PK Correlation

Geometry Mathnasium Material NT Correlation


Unit 1:


Section 1.1 Symmetry

  • Line Symmetry - PK3514

  • Point Symmetry - 

  • Rotational Symmetry - PK3104

  • Translational Symmetry - PK3104

Section 1.2 So, What’s the Point

  • Definition of a point - PK824

  • Definition of a plane - PK824

  • Definition of a line - PK824

  • Definition of a segment - PK824

  • Definition of a ray - PK824

  • Union/Intersection - PK824

  • Locus of Points/Endpoints - FO2160

Section 1.3 Nspire Intro


Section 1.4 Transformations 

  • Isometries {Translation PK3509, Rotation PK3510, Reflection PK3511, Dilation PK3512}

  • Dilations

  • Pre-image/image (Steps to transformation) - PK3581

Section 1.5 Transformations by Hand

  • Translating by vectors

  • Reflecting across lines - PK3584

  • Rotating around a central point

  • Dilating from point - PK3583


Unit 2: Transformations with Coordinates


Section 2.1 Transformations

  • Graphing points/ translating points - PK3509

  • Reflecting, rotating, dilating on the graph - PK3511, PK3512

Section 2.2 Things I Learned in Algebra

  • Midpoints - PK3434

  • Length of segments - PK3435

  • Slopes of lines - PK3408

Section 2.3 More Geometry and Algebra!

  • Altitudes - PK3552

  • Perpendicular Bisectors - PK3552

  • Medians - PK3552

Section 2.4 One Magic Moment, One Magical Point

  • Solving systems of linear equations/finding the intersection of lines - {Substitution PK3417, Elimination PK3418, Graphing PK3416, Problem-Solving PK3452}

  • Reflecting points over oblique lines - PK3584

  • Determining medians/perpendicular bisectors on shapes graphically

  • Distance between two lines - 

Unit 3: Congruent Triangles



Section 3.1 It’s Only Logical

  • Conditional Statements - PK3530

Section 3.2 Three is a Magic Number

  • AAS, SAS, SSS, ASA - PK4571, PK4570

  • Describing transformations

Section 3.3 Congruent Triangles

  • Vertical Angles - PK3580, PK3572, PK3573

  • Reflexive Property  - PK3533

  • Transitive Property - PK3533

  • Two-column proofs - PK3533

Section 3.4 Supps and Comps

  • Complementary angles - PK3507

  • Supplementary angles - PK3507

  • Corresponding supp/comp proof reasons

Section 3.5 Addition and Subtraction

  • Addition theorem - PK3566

  • Subtraction theorem

Section 3.6 Multiplication and Division

  • Multiplication theorem

  • Division theorem


Unit 4: Constructions


Section 4.1: The Basics

  • Copying a segment - FO0023

  • Adding segments - FO0023

  • Copying an angle - FO0023

  • Bisecting an angle - FO0023

  • Constructing SSS triangle

  • Triangle Inequality Theorem

Section 4.2: Constructing Perpendiculars

  • Constructing a perpendicular bisector - FO0023

  • Construct a perpendicular to a segment - FO0023

  • Construct a perpendicular to a line through a point not on the line

Section 4.3 Points of Concurrency

  • Point of concurrency - PK3559

  • Incenter - PK3559

  • Circumcenter - PK3559

  • Centroid - PK3559

  • Orthocenter - PK3559


Unit 5: Proving Triangles Congruent is Not the Goal, It’s the Process


Section 5.1: The End of CPCTC

  • “CPCTC” - PK3573 (page 6)

  • Circles - Congruent Radii

Section 5.2: Turn It Up To 11: Draw a line & overlapping triangles

Section 5.3: Classify Triangles

  • The sum of triangle angles equals 180

  • Equilateral, Isosceles, Scalene - PK3099

  • Acute, Right, Obtuse Triangles - FO111

  • The longest side is opposite the largest angle

Section 5.4: My Favorite Theorems

  • Isosceles - base angle/base sides

  • Isosceles - angle bisector = median = altitude

Section 5.5: RHL

  • RHL Proof


Unit 6: The Next Chapter


Section 6.1: The Questions of Mathematics

  • If two angles supp and comp -> rt angles

Section 6.2: No Picture? Then Make a Picture

  • Draw it out

Section 6.3: Perpendicular Bisector and Equidistance

  • If a pt is on the perp bisector, it is central to the endpoints

  • If two points are equidistant to the endpoints of a seg -> they form the perp bisector

Section 6.4: If It’s Not This, Then It’s Got To Be This 404

  • Proof by Contradiction


Unit 7: Lines, Angles, Quads


Section 7.1: Parallel Lines

  • Transversal

  • Alternate Interior Angles, Alternate Exterior Angles, Corresponding Angles, Same Same Interior Angles - FO272

Section 7.2: Parallel Lines Keep Going

  • Constructing parallel lines

Section 7.3: Quadrilaterals

  • Definition of a quadrilateral

  • Properties of a parallelogram

  • Properties of a kite

  • Properties of a rectangle

  • Properties of a rhombus

  • Properties of a square

  • properties of a trapezoid

  • Properties of a isosceles trapezoid - PK3099

Section 7.4: More Quadrilaterals

  • Solving problems involving properties of quads

Section 7.5: It looks like a parallelogram

  • Properties of a parallelogram

    • Both pairs of opposite sides are parallel

    • Both pairs of opposite sides are congruent

    • Both diagonals bisected

    • Same pair of opposite sides and congruent = parallelogram

    • The sum of angles in quadrilaterals is 360. 

Section 7.6: Special Quads

  • Solving problems using obscure properties of quads.


Unit 8: Similarity


Section 8.1: Dilations

Section 8.2: Dilations pt. Deux

Section 8.3: Similarity

Section 8.4: Proving Similar Triangles

Section 8.5: Proportions Without Similar Triangles


Unit 9: Right Triangles


Section 9.1: Rt Triangle inside a Rt Triangle

Section 9.2: Pythagorean Theorem - PK3363

Section 9.3: Right Triangle Families - PK3363

Section 9.4: Rt Triangles in 3D Figures - 

Section 9.5: Special Right Triangles - PK3561

Section 9.6: Right Triangle Trigonometry - PK3916

Law of Cosines - PK3914, PK3915

Law of Sines - PK3913, PK3915


Unit 10: Polygons


Section 10.1: Polygon Formulas - PK3501, PK3550, PK3551

Section 10.2: What is Regular? - PK3501

Section 10.3: Constructing of Regular Polygons - FO 023 (page 29)

Section 10.4: Tessellations - FO 194


Unit 11: Circles


Section 11.1: Chords of Circles - PK3562

Section 11.2: From the Center to the Arc 

Section 11.3: Tangents - PK3569

Section 11.4: Angle-Arc Relationships - PK3568

Section 11.5: Arcs have Length and Measure - PK3588

Section 11.6: Power of the Poin 


Unit 12: Area

Section 12.1: Area Basics - PK3089

Section 12.2: More Area Formulas - PK3362(Rectangles), PK3364(Triangles), PK3365(Circles), PK3523(Parallelograms), PK3524(Trapezoids)

Section 12.3: Regular Polygons - PK3590

Section 12.4: Sectors of Circles - PK3588

Section 12.5: Ratios of Areas - PK3582


Unit 13: 3D

Section 13.1: Lines and Planes in Space - PK0804 (skew lines)

Section 13.2: If You Look At It That Way - ???

Section 13.3: Cross-Sections of 3D Objects - FO 242, FO 188


Unit 14: Surface Area and Volume


Section 14.1: Surface Area - PK3527, PK3595

Section 14.2: SA of Cylinders and Cones - PK3527, PK3595

Section 14.3: Volume Basics - PK3528, PK3596

Section 14.4: Volumes with an Apex - PK3528, PK3596

Section 14.5: Spheres - PK3555


Unit 15: Modeling - Difficult to find any Mathnasium material with geometric monitoring. PK3534 and PK3535 have some geometric problem-solving


Section 15.1: Intro to Modeling

Section 15.2: Art Gallery Watchmen

Section 15.3: Packaging and Packing

Section 15.4: Airports





 

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