Common Core State Standards for Mathematics
Grade 8
Geometry
Understand and apply the Pythagorean Theorem.
8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Ohio Mathematics Academic Content Standards (2001)
Geometry and Spatial Sense Standard
Benchmarks (5–7)
G.
Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles.
Benchmarks (8–10)
H.
Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.
Grade Level Indicators (Grade 7)
3.
Use and demonstrate understanding of the properties of triangles. For example:
a. Use Pythagorean Theorem to solve problems involving right triangles.
b. Use triangle angle sum relationships to solve problems.
Grade Level Indicators (Grade 8)
1.
Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.
Grade Level Indicators (Grade 10)
3.
Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including:
a. prove the Pythagorean Theorem;
b. prove theorems involving triangle similarity and congruence;
c. prove theorems involving properties of lines, angles, triangles and quadrilaterals; and
d. test a conjecture using basic constructions made with a compass and straightedge or technology.
Principles and Standards for School Mathematics
Geometry Standard
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
Expectations (6–8)
create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
Expectations (9–12)
establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others;