Geometry EOC Review Notes

Circles, Geometric Measurement, and Geometric Properties

MAFS.912.G-C.1.1 EOC Practice

• Key Concepts:
  • All circles are similar.
  • Use sequence of transformations to prove similarity of circles.
  • Similarity can be determined using measures of different parts of a circle.
  • Prove similarity by transformations or by explaining proportional relationships.
• Questions:
  1. Transformation explanation for similarity between circles A and B.
  2. Sequence of similarity transformations for mapping circles.
  3. Explanation for why all circles are similar.
  4. Methods to prove circle similarity.
  5. Truth about ratios of areas, circumferences, and radii of circles.

MAFS.912.G-C.1.2 EOC Practice

• Key Concepts:
  • Solve problems using properties of central angles, diameters, and radii.
  • Include inscribed angles, circumscribed angles, and chords.
  • Use properties involving tangents.
• Questions:
  1. Solve for angle based on given central angle.
  2. True statements about triangle formed with tangent and circle.
  3. Measure of angle given in a circle.
  4. Identifying incorrect information in a diagram.
  5. Length calculation in intersecting chords.
  6. Solving for unknown angles and measures in circle problems.

MAFS.912.G-C.1.3 EOC Practice

• Key Concepts:
  • Identify inscribed and circumscribed circles of a triangle.
  • Construct or provide steps for constructions of these circles.
  • Use properties of angles for inscribed quadrilaterals.
  • Prove angle properties using inscribed circles.
• Questions:
  1. Construction of inscribed circle and identifying its center.
  2. Properties and construction of circumscribed circles.
  3. Proving supplementary angles in inscribed quadrilaterals.
  4. Validity of inscribing given quadrilaterals in a circle.

MAFS.912.G-C.2.5 EOC Practice

• Key Concepts:
  • Identify sector area of a circle as a proportion of the entire circle.
  • Solve problems using arc length, radius, and radian measure.
  • Derive formula for sector area.
  • Prove arc length proportionality.
• Questions:
  1. Find the area of a sector given specific circle dimensions.
  2. Calculate arc lengths and justify with calculations.

MAFS.912.G-GMD.1.1 EOC Practice

• Key Concepts:
  • Argue formulas for circumference and area of circles.
  • Use dissection arguments for volume in cylinders and cones.
  • Informal limit arguments for circle area and volume.
• Questions:
  1. Estimation methods using sectors and shapes resembling rectangles.
  2. Volume calculation using pyramids and prisms.
  3. Use of Cavalieris principle for equal volume demonstration.

MAFS.912.G-GPE.1.1 EOC Practice

• Key Concepts:
  • Determine center and radius from circle equations.
  • Complete square to find circle parameters.
  • Derive circle equations using Pythagorean theorem.
• Questions:
  1. Calculate center and radius from given circle equations.
  2. Derive equations using coordinates and given conditions.
  3. Analyze circle properties and characteristics based on equations.

MAFS.912.G-GPE.2.4 EOC Practice

• Key Concepts:
  • Use coordinates to prove properties of geometric figures.
  • Analyze and provide arguments for geometric theorems.
  • Prove properties of polygons using coordinates.
• Questions:
  1. Proving geometric properties such as parallelogram characteristics.
  2. Use of coordinates to substantiate geometric figures and their properties.

MAFS.912.G-GPE.2.5 EOC Practice

• Key Concepts:
  • Focus on parallel and perpendicular line equations.
  • Formulate lines equations from given points or conditions.
  • Prove slope criteria for line relationships.
• Questions:
  1. Identifying line relationships from given equations.
  2. Formulating equations based on slope conditions and points.
  3. Proofs and validations of line properties.

This review covers extensive foundational concepts and problem-solving strategies in understanding geometric properties, focusing on circles, angles, transformations, and coordinate-based proofs. The exercises span a wide range of concepts from determining simple measures to complex derivations and proofs.