CCSS.Math.Content.HSG-GPE.B.4
The Standard
Use coordinates to prove simple geometric theorems algebraically.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use slope, distance, midpoint, and coordinate equations to test geometric claims. They show calculations, connect each result to a geometric property, and conclude whether the claim is true or false.
What Mastery Looks Like
- Students select properties that are enough to prove a claim, such as parallel opposite sides and one right angle for a rectangle. They organize exact calculations and state how each result supports the conclusion.
Common Misconceptions
- Students may treat equal slopes as proof of perpendicular lines instead of parallel lines, or forget that perpendicular slopes are negative reciprocals. They may connect points in the wrong order, rely on the drawing, or round radicals before checking an equation.
How to Assess It
- Give points A(0,0), B(3,1), C(2,4), and D(-1,3). Ask students to decide whether ABCD is a rectangle and justify the answer with slope calculations.
Lesson moves
Ways to Teach It
Plot four coordinate cards on graph paper, connect them in order, then use slope and distance calculations to classify the quadrilateral.
Write which measurements would prove a quadrilateral is a rectangle, then compare a slope proof with a distance proof.
Play proof-card match: pair each geometric claim with the slope, midpoint, distance, or equation calculation that verifies it.
Use four corner coordinates from a floor plan to check whether a proposed room is rectangular before calculating flooring area.
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Printable HSG-GPE.B.4 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-GPE.B.4, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.8.G.B.8
Coordinate proofs often use distances from the Pythagorean Theorem to show congruent lengths and classify figures.
- CCSS.Math.Content.8.EE.B.6
Coordinate proofs often use slope and line equations to show collinearity, parallel sides, or intercept relationships algebraically.
- CCSS.Math.Content.HSG-CO.A.1
Coordinate proofs often use definitions of parallel, perpendicular, line segment, and circle, but students can learn these within analytic geometry.
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