Rise and Sine

10 Geometry Theorem Proofs You Need to Teach Your Students

Geometry theorem proofs have a reputation. Not a good one. I’m not sure where the bad reputation came from, but teaching geometry theorem proofs does not have to be miserable! And most importantly, you’re students can succeed in learning them!

Tell me if this sounds familiar. In every geometry class, once the teacher mentions the word “proof”, and an agonizing groan echoes throughout the building. 

I know you can relate!

Let’s chat about what geometry theorem proofs you should cover in class and some ways you can engage your class. 

10 Geometry Theorems to Prove if You Follow CCSS (and even if you don’t!)

geometry theorem proof checklist
  • The Vertical Angle Theorem
  • The Triangle Angle Sum Theorem
  • The Isosceles Triangle Theorem
  • The Perpendicular Bisector Theorem
  • The Alternate Interior Angle Theorem

The following theorems on parallelograms:

  • Opposite sides of a parallelogram are congruent
  • Opposite angles of a parallelogram are congruent
  • Diagonals of a parallelogram bisect each other
  • A parallelogram with congruent diagonals is a rectangle


  • All circles are similar

How to Teach Geometry Theorem Proofs

Hype up those proofs! They are just a puzzle, with a twist of math. To start, we have information about the theorem and at the end, we know what the theorem needs to show. Everything in between is pieces that put that puzzle together. 

Try a cut and paste activity. Provide the statements and the reasons for the students to analyze and formulate the proof with. 

Alternatively, go digital with these drag and drop activities that will do the same! Easy to assign, great to revisit throughout the year, and NO mess and NO prep!

image to show example of drag and drop geometry theorem proof

You can differentiate proofs so easily!

Here are some options to consider depending on the needs of the students in your classroom:

  • 1: Provide the statements and have the students write the reasons (or a mix and match).
  • 2: Use a cut and paste or drag and drop activity. 
  • 3: Create the proof from scratch.

What are your favorite geometry theorem proofs to cover? Do you have a favorite way to teach them with your students?

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