Common Core · High school
HSG-GPE.B.4
High school — Use coordinates to prove simple geometric theorems algebraically.
High school — Use coordinates to prove simple geometric theorems algebraically, for example that a figure defined by four given points is a rectangle.
High school — Use coordinates to prove simple geometric theorems algebraically, for example that a given point lies on a given circle.
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 →
- Polygons & QuadrilateralsFind the angle sums of any polygon, use the properties of parallelograms, rectangles, rhombi, squares, trapezoids and kites, and classify a quadrilateral from what is known about it.Read the lesson →
- Equations of CirclesWrite the equation of a circle from its centre and radius, read the centre and radius back from an equation, complete the square to find them, and test whether a point lies on the circle.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.
- Find the interior and exterior angle sums of a polygon and each angle of a regular one.
- Use the side, angle and diagonal properties of a parallelogram to find unknowns.
- Apply the special properties of rectangles, rhombi, squares, trapezoids and kites.
- Classify a quadrilateral from a list of its properties, choosing the most specific name.
- Write the equation of a circle from its centre and radius, or from its centre and a point on it.
- Read the centre and radius from (x - h)2 + (y - k)2 = r2.
- Complete the square to rewrite x2 + y2 + ax + by + c = 0 in centre-radius form.
- Decide whether a point lies on, inside or outside a circle.