Lesson 12

Proofs about Quadrilaterals

Lesson Narrative

In a previous lesson students used strips and fasteners to make conjectures and practice proofs about quadrilaterals. In this lesson students prove the important result that all rectangles are parallelograms. Then groups of students tackle different relationships among quadrilaterals and their diagonals. This requires reasoning from definitions such as:

  • rectangle is a quadrilateral with four right angles.
  • rhombus is a quadrilateral with four congruent sides.

Throughout the lesson students move from making conjectures, to making specific statements to be proved, to writing a proof, to critiquing a proof. When students have to determine the given information and draw their own diagram students are making sense of problems (MP1).

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.

Learning Goals

Teacher Facing

  • Comprehend a conjecture and express it (in writing) as a specific statement to prove.
  • Critique others' reasoning (in spoken and written language) about quadrilaterals.
  • Prove (in writing) theorems about quadrilaterals.

Student Facing

  • Let’s prove theorems about quadrilaterals and their diagonals.

Learning Targets

Student Facing

  • I can critique a proof about quadrilaterals.
  • I can prove theorems about quadrilaterals.
  • I can rewrite a conjecture so it is specific enough to prove.

CCSS Standards

Building On


Building Towards

Glossary Entries

  • rectangle

    A quadrilateral with four right angles.

  • rhombus

    A quadrilateral with four congruent sides.