Use coordinates to describe the effect of transformations (dilations, translations, rotations, reflections). (8.G.3)
Apply the Pythagorean Theorem in mathematical problems, including those in real-world contexts. (8.G.7)
Concepts and Skills
* Rotations, reflections, translations
* Prove congruency using transformations
* Prove similarity using dilations and transformations
* Apply the Pythagorean Theorem (e.g., missing triangle side lengths, distance between two points)
Describe and analyze symmetries of figures
A student in 8th grade will demonstrate the ability to apply and comprehend critical language by describing the effect of transformations, and by explaining the Pythagorean Theorem.
Right triangles have a unique and important side-length relationship known as the Pythagorean Theorem.
Knowing and applying geometric properties and equations allows one to solve complex problems involving geometric figures.
Factual Guiding Questions
What is the difference between each type of transformation?
What is the Pythagorean Theorem?
How do you find the distance between two points?
How do you determine if two figures are similar?
How can you identify which transformations have been made to create a figure?
Conceptual Guiding Questions
What specific information about distances can we use when we transform a figure?
What properties can be used to determine if two figures are similar?
How can it be determined whether or not a triangle is a right triangle if only the side lengths are known?
Engaging/Debatable Guiding Questions
When is it appropriate and useful to use the Pythagorean Theorem?
What connections exist between geometry and algebra?