Common Core · High school
HSG-GPE.B.5
High school — Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
High school — Prove and use the slope criteria for parallel and perpendicular lines.
High school — Use the slope criteria for parallel and perpendicular lines to find the equation of a line parallel or perpendicular to a given line through a given point.
The 3 skills that cover it
- Coordinate GeometryUse the distance, midpoint and slope formulas to measure and classify figures drawn on the coordinate plane, and to prove that lines are parallel or perpendicular.Read the lesson →
- Linear FunctionsWork with straight lines: slope as a rate of change, intercepts, and the equation y = mx + b.Read the lesson →
- Forms of a LineWrite the equation of a line in point-slope, slope-intercept and standard form, convert between the three, read intercepts off standard form, and build parallel and perpendicular lines through a point.Read the lesson →
What a student should be able to do
- Find the midpoint of a segment and the distance between two points.
- Use slopes to decide whether two segments are parallel, perpendicular or neither.
- Find the point that divides a segment in a given ratio.
- Classify a triangle or quadrilateral from the coordinates of its vertices and find its perimeter or area.
- Compute the slope between two points.
- Write the equation of a line from a slope and a point.
- Interpret slope and intercept in a real-world context.
- Identify parallel and perpendicular slopes.
- Write the equation of a line from a point and a slope in point-slope form, and from two points.
- Convert between slope-intercept form y = mx + b and standard form Ax + By = C.
- Find both intercepts of a line given in standard form.
- Write the equation of the line through a point that is parallel or perpendicular to a given line.