CCSS.Math.Content.HSG-GPE.B

CCSS.Math.Content.HSG-GPE.B is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSG-GPE.B.4

  Use coordinates to prove simple geometric theorems algebraically.

• CCSS.Math.Content.HSG-GPE.B.5

  Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicu...

• CCSS.Math.Content.HSG-GPE.B.6

  Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

• CCSS.Math.Content.HSG-GPE.B.7

  Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

01

What Students Need to Do

Students place geometric figures on a coordinate plane and use algebra to justify claims about them. They use slope, distance, and midpoint calculations to prove relationships such as parallel lines, equal sides, or bisected segments.

02

What Mastery Looks Like

A student can choose helpful coordinates and correctly apply slope, distance, and midpoint formulas. They show each calculation and connect the result to the geometric claim.

03

Common Misconceptions

Students often treat a picture or measured lengths as proof. They may mishandle vertical lines, confuse opposite reciprocal slopes, or forget to square both coordinate differences in the distance formula.

04

How to Assess It

Exit ticket: Given A(-2, 0), B(2, 0), and C(0, 3), prove triangle ABC is isosceles using algebra.

1. 01

   Students plot a quadrilateral on graph paper, measure its sides, then confirm its type using slopes and distances.

2. 02

   Ask students to write which coordinates would make proving a rectangle easiest, then explain why.

3. 03

   Run a proof card sort matching geometric claims with slope, midpoint, or distance calculations.

4. 04

   Use coordinates from a simple park map to verify that paths are parallel, perpendicular, or equal in length.

• CCSS.Math.Content.HSG-CO.C.9

  Prove theorems about lines and angles.

• CCSS.Math.Content.HSG-CO.C

  Prove geometric theorems

• CCSS.Math.Content.HSG-SRT.B

  Prove theorems involving similarity