Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Proofs about parallelograms
Prove parallelogram and rectangle side angle and diagonal properties
Problem types
- Trapezoid midsegment, base angles and diagonals
- Quadrilateral conditions and trapezoid angles
- Angles in a parallelogram with a perpendicular
- Use parallelogram and rectangle theorems
- Complete a parallelogram proof
- Put a parallelogram proof in order
- Theorem or converse: audit a parallelogram argument
- Condition that makes a parallelogram a rhombus or a rectangle
- Show the work: an angle in a parallelogram with a perpendicular segment
Builds on
- Congruence criteria for triangles
- Writing and critiquing a geometric proof
- Categories and subcategories of shapes · Useful idea
If every rectangle is a parallelogram, it inherits the properties of parallelograms. Proofs use this to transfer facts between classes.
Leads to
- Proofs that use coordinates · See it applied
Bisecting diagonals and congruent rectangle diagonals become coordinate tests: compare midpoints of diagonals and diagonal lengths.
- Matrices as transformations of the plane · See it applied
A matrix maps the unit square to a parallelogram, and the area of that parallelogram is the determinant.
Related skills
- Vectors and their components · Related idea
Opposite sides of a parallelogram are equal vectors, so the diagonals are the sum and difference of two adjacent side vectors.
- Proofs about triangles · Shared foundations
- Theorems about circles · Shared foundations
- Proofs about lines and angles · Shared foundations
- Why the circle and solid formulas hold · Shared foundations
Open the interactive map to explore lessons and skill connections.