8.G - Geometry

From EngageNY

Understand congruence and similarity using physical models, transparencies, or geometry software.
  1. Verify experimentally the properties of rotations, reflections, and translations:
    • Lines are taken to lines, and line segments to line segments of the same length.
    • Angles are taken to angles of the same measure.
    • Parallel lines are taken to parallel lines.
  2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
  3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
  4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
  5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
Understand and apply the Pythagorean Theorem.
  1. Explain a proof of the Pythagorean Theorem and its converse.
  2. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
  3. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
  1. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Supporting Materials

ebook

What's Your Angle, Pythagoras?

Young Pythagoras can't seem to stay out of trouble. Every time he tries to help, people get angry. What's a curious kid to do?


On a trip to Egypt, Pythagoras' curiosity helps him discover the secret of the right triangle. A clever introduction to the Pythagorean Theorem.

Learn more on Engage NY

EngageNY.org is developed and maintained by the New York State Education Department (NYSED) to support the implementation of key aspects of the New York State Board of Regents Reform Agenda.

This is the official web site for current materials and resources related to the Regents Reform Agenda. The agenda includes the implementation of the New York State P-12 Common Core Learning Standards (CCLS), Teacher and Leader Effectiveness (TLE), and Data-Driven Instruction (DDI). EngageNY.org is dedicated to providing educators across New York State with real-time, professional learning tools and resources to support educators in reaching the State’s vision for a college and career ready education for all students.