CCSS.Math.Content.HSG-GPE.B.4
The standard
Use coordinates to prove simple geometric theorems algebraically.
Common Core State Standards for Mathematics
What this standard means
Students need to use coordinate facts as evidence. They should find slopes, distances, midpoints, and equations, then connect those results to a geometric claim. For example, they may show sides are parallel, sides are perpendicular, diagonals bisect each other, or a point fits a circle equation.
Mastery looks like a clear algebraic proof with labeled calculations and a final conclusion tied to the shape or theorem. Students often get stuck choosing the right test, such as slope versus distance, or they calculate correctly but never explain what the numbers prove.
Ways to teach it
- Give pairs four plotted points on graph paper and have them prove whether the figure is a rectangle using slopes and distances.
- Ask students to write: What algebraic evidence would convince you that a quadrilateral is a parallelogram but not a rectangle?
- Use an exit ticket with three points and ask students to decide if they form a right triangle, showing slope work.
- Have students check whether a phone map location lies within a circular delivery zone by using the distance formula.
Plan a lesson for CCSS.Math.Content.HSG-GPE.B.4
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Related standards
- CCSS.Math.Content.HSG-CO.C.9
Prove theorems about lines and angles.
- CCSS.Math.Content.HSG-CO.C.10
Prove theorems about triangles.
- CCSS.Math.Content.HSG-CO.C
Prove geometric theorems
- CCSS.Math.Content.HSG-GPE.B
Use coordinates to prove simple geometric theorems algebraically