SY26 Geometry EOC Review Materials Notes

SY26 Geometry EOC Review Overview

  • Project Name: SY26 Geometry EOC Review Materials.

  • Primary Purpose: A definitive guide for university students or high school students preparing for the Geometry End-of-Course (EOC) examination.

  • Essential Resources:     - Student Version EOC Review Packet: The core practice document for the curriculum.     - Brain Dump Sheet: A consolidated reference for all memorization-heavy content.     - Video Lesson Link: Instructional support for all practice items.     - EOC Calculator: The approved computational tool for the examination.     - EOC Review KEY: The final answer key for verification.

Geometric Reasoning: Foundations, Angles, and Triangles

  • Standard 912.GR.1.1 (Items 1, 2, and 3): Midpoints and Angles     - Midpoint of a Line: Focuses on the calculation of the middle point of a line segment. The formula for the midpoint $M$ of a segment with endpoints (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by:     - M=(x1+x22,y1+y22)M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)     - Angles Cheat Sheet: A comprehensive guide to angle classifications (acute, obtuse, right, straight) and angle pair relationships (supplementary, complementary, vertical).

  • Standard 912.GR.1.2 (Item 1): Parallel Lines     - Parallel Lines Vocab Handout: Covers terminology related to transversals crossing parallel lines, including:         - Alternate Interior Angles         - Alternate Exterior Angles         - Consecutive Interior Angles         - Corresponding Angles

  • Standard 912.GR.1.3 (Item 1) and 912.GR.1.4 (Item 1): Quadrilaterals and Triangle Midsegments     - Quadrilaterals Handout: Detailed properties of parallelograms, rectangles, rhombi, squares, and trapezoids.     - Triangle Midsegment Handout: Describes the segment connecting the midpoints of two sides of a triangle, which is parallel to the third side and half its length.     - Lengthmidsegment=12(Lengthbase)Length_{midsegment} = \frac{1}{2}(Length_{base})

  • Standard 912.GR.1.5 (Item 1): Trapezoid Geometry     - Trapezoid Midsegment Handout: Focuses on the median of a trapezoid. The length of the midsegment mm of a trapezoid with bases b1b_1 and b2b_2 is:     - m=b1+b22m = \frac{b_1 + b_2}{2}

  • Standard 912.GR.1.6 (Items 1 and 2): Congruence and Similarity     - Triangle Congruence Theorems and Cheat Sheet Handout: Covers criteria including SSS, SAS, ASA, AAS, and HL.     - Triangle Similarity Rules and Worked Examples Handout: Covers criteria such as AA~, SSS~, and SAS~.

Transformations and Rigid Motion

  • Standard 912.GR.2.1 (Item 1): Classifying Transformations     - Types of Transformations Study Guide: An exhaustive guide covering isometries (rigid motions) and non-isometries.

  • Standards 912.GR.2.2, 912.GR.2.3, 912.GR.2.5, 912.GR.2.6, and 912.GR.2.8: Rigid Motion Rules     - Geometry Rigid Transformation Rules Quick Reference Sheet: Provides the coordinate notation for various transformations:         - Translations: (x,y)→(x+a,y+b)(x, y) \rightarrow (x + a, y + b)         - Reflections: Over axes (xx-axis: (x,−y)(x, -y); yy-axis: (−x,y)(-x, y)) or lines such as y=xy = x ((y,x)(y, x)).         - Rotations: Center at origin for 90∘90^\circ, 180∘180^\circ, and 270∘270^\circ.

Coordinate Geometry and Partitioning

  • Standard 912.GR.3.1, 912.GR.3.2 (Item 1): Partitions     - Partitions Resource: Explains how to find a point that divides a directed line segment into a specific ratio k=mm+nk = \frac{m}{m+n}.     - x=x1+k(x2−x1)x = x_1 + k(x_2 - x_1)     - y=y1+k(y2−y1)y = y_1 + k(y_2 - y_1)

  • Standard 912.GR.3.2 (Item 2) and 912.GR.3.3 (Item 1): Quadrilaterals in the Coordinate Plane     - Quadrilaterals Handout: Used here to verify shapes on a coordinate grid using slope (to prove parallelism/perpendicularity) and distance.

  • Standard 912.GR.3.4 (Item 1): Distance in 2D Space     - Distance Formula: The formula used to find the length between points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2).     - d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Three-Dimensional Geometry and Measurement

  • Standard 912.GR.4.1 (Item 1): Cross Sections     - Cross Sections Practice Problems: Exercises involving slicing 3D solids (prisms, pyramids, cones, cylinders) to identify the resulting 2D shapes.

  • Standard 912.GR.4.2 (Item 1): Solids of Revolution     - Rotate 2D Shapes Practice Problems: Covers the generation of 3D solids by rotating 2D figures around an axis (e.g., rotating a rectangle to create a cylinder).

  • Standard 912.GR.4.3 (Item 1): Surface Area and Volume Mastery     - IXL Video and Practice Problems (U.11): Focused specifically on the surface area of complex and simple solids.

  • Standard 912.GR.4.4 (Item 1): Density     - Density Practice: Application of formulas relating mass, volume, and density.     - Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}

  • Standards 912.GR.4.5 (Item 1) and 912.GR.4.6 (Item 1): 3D Formulas     - Surface Area and Volume Formulas: High-level reference for spheres, cones, cylinders, prisms, and pyramids.

Geometric Constructions

  • Standard 912.GR.5.1 (Item 1): Angle Copying     - Copying an Angle Instructions Handout: Step-by-step procedural guide using a compass and straightedge.

  • Standard 912.GR.5.2 (Item 1, Parts A and B): Angle Bisection     - Bisecting an Angle Instructions Handout: Procedural guide for dividing an angle into two congruent parts.     - Review of all Constructions: Comprehensive recap of segments, angles, parallel lines, and perpendicular bisectors.

  • Standard 912.GR.5.3 (Item 1): Triangles and Circles     - Circumcircle of a Triangle: Instructions for constructing the circle that passes through all vertices of a triangle using the intersection of perpendicular bisectors (the circumcenter).

Circles: Properties and Equations

  • Standards 912.GR.6.1, 912.GR.6.2, and 912.GR.6.3 (Items 1 and 2): Comprehensive Circle Theory     - Everything You Need to Know About Circles: Document covering tangents, secants, chords, arcs, central angles, and inscribed angles.

  • Standard 912.GR.6.4 (Item 1): Area and Sectors     - Area of Circles/Sectors Practice Problems: Focuses on finding the area of a portion of a circle.     - Area of Sector=θ360∘×πr2\text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2

  • Standards 912.GR.7.2 (Items 1 and 3) and 912.GR.7.3 (Items 1 and 2): Coordinate Geometry of Circles     - Circle Equations Lesson: In-depth study of the standard form of a circle equation with center (h,k)(h, k) and radius rr.     - (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2     - Khan Academy: Circle Review: External digital review for mastering equations and graphing.

Logic and Trigonometry

  • Standard 912.LT.4.3 (Item 1): Logic     - Conditional Statements Study Guide: Covers "If-Then" statements, inverses, converses, and contrapositives.

  • Standard 912.LT.4.10 (Item 1): Logic Applications     - Quadrilaterals Handout: Utilized here for logical proofs and property classifications.

  • Standards 912.T.1.1 (Items 1 and 2) and 912.T.1.2 (Items 1 and 2): Trigonometry     - Sin, Cosine, Tangent Review: Definitive study on SOH-CAH-TOA relationships in right triangles.     - sin⁡(θ)=OppositeHypotenuse\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}     - cos⁡(θ)=AdjacentHypotenuse\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}     - tan⁡(θ)=OppositeAdjacent\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}     - This section also addresses using inverse trigonometric functions to find unknown angle measures.