Geometry Regents Review (June 2, 2022) - Live on YouTube

Overview

• Presenter: Kirk Weiler
• Topic: Reviewing June 2022 Geometry Regents Exam
• Target Audience: Students in New York preparing for Geometry Regents
• Materials Needed: Previous June 2022 exam, calculator (preferably TI Inspire)

Exam Format

• Part 1: 24 multiple-choice questions (2 points each, no partial credit)
• Part 2: Seven questions worth two points each
• Part 3: Three questions worth four points each
• Part 4: One question worth six points

Key Concepts Reviewed

Problem 1: Dilation and Coordinates

• Topic: Dilation centered at the origin
• Steps:
  1. Multiply coordinates by dilation constant (k)
  2. Given A' from A, find k (here, k = 2)
  3. Apply k to another point to find its image
• Example: A = (-2, 1), A' = (-4, 2) ⇒ k = 2
• New coordinates: B = (2, 4) ⇒ B' = (4, 8)

Problem 2: Cross Section of Pyramid

• Concept: Slicing a pyramid parallel to the base results in a shape similar to the base.
• Example: Square pyramid, sliced parallel to base, produces a square.

Problem 3: Right Triangle Trigonometry and Similarity

• Concept: Using trig ratios (sine, cosine, tangent) for similar triangles
• Significance: Apply similarity to understand relationships in the triangles
• Mnemonic: SOHCAHTOA

Problem 4: Rotational Symmetry

• Figure: Regular Pentagon
• Concept: Minimum rotation to map figure onto itself is based on dividing 360° by the number of sides
• Example: Pentagon (5 sides), 360°/5 = 72°

Problem 5: Rigid Motions

• Recognizing Transformations: Matching figures to congruent images via reflection, rotation, translation
• Orientation: Reflections change vertex ordering (clockwise to counterclockwise)

Problem 6: Interior and Exterior Angles, Similarity

• Figure: Used for identifying transformations affecting angles and proving similarity through proportions and trig ratios

Problem 7: Parallelogram Proofs

• Properties of Parallelograms: Opposite sides are parallel and equal; diagonals bisect each other

Problem 8: Volumes of Revolution

• Concept: Rotating a right triangle around an axis to form 3D shapes like cones or cylinders
• Example: Right triangle rotated around the hypotenuse forms a cone

Problem 9: Proof of Parallelogram

• Given: Diagonals intersecting lines proving parallel properties
• Proof: Using corresponding or alternate interior angles to prove parallelism

Problem 10: Coordinate Geometry - Transformations

• Transformations: Translate, reflect, and rotate points and figures on coordinate plane
• Example: Line dilated by factor affects its position

Specific Problems Discussed

1. Problem 11: Proving point on intersecting lines results in specific coordinate translations
2. Problem 12: Volumes and mass calculations involving density and material needs (e.g., concrete mix calculations for footings)
3. Problem 13: Identifying transformations that preserve distance through algebraic rules
4. Problem 14: Geometric proofs and constructions - identifying right angles, parallel lines, isosceles triangles, and properties of similar figures

Strategies and Tips

• Understand and apply properties of geometric figures: parallelograms, triangles, circles, and polygons
• Use SOHCAHTOA for right-triangle trigonometry problems
• Pay attention to transformation definitions (reflection, rotation, translation)
• Practise identifying figures' properties through proofs and coordinate geometry
• Utilize given formula sheets for volume, area, and other geometric calculations

Conclusion

• Kirk Weiler emphasizes understanding the geometric principles and consistent practice with problems similar to those on the Regents exam. The lesson aims at improving problem-solving skills and confidence in tackling various geometric problems on the day of the exam.