Make a game plan. Try to figure out how to get from the givens to the prove conclusion with a plain English, commonsense argument before you worry about how to write the formal, twocolumn proof.
Make up numbers for segments and angles. During the game plan stage, it's sometimes helpful to make up arbitrary lengths for segments or measures for angles. Doing the math with those numbers (addition, subtraction, multiplication, or division) can help you understand how the proof works.
Look for congruent triangles (and keep CPCTC in mind). In diagrams, try to find all pairs of congruent triangles. Proving one or more of these pairs of triangles congruent (with SSS, SAS, ASA, AAS, or HLR) will likely be an important part of the proof. Then you'll almost certainly use CPCTC on the line right after you prove triangles congruent.
Try to find isosceles triangles. Glance at the proof diagram and look for all isosceles triangles. If you find any, you'll very likely use the ifsidesthenangles or the ifanglesthensides theorem somewhere in the proof.
Look for parallel lines. Look for parallel lines in the proof's diagram or in the givens. If you find any, you'll probably use one or more of the parallelline theorems.
Look for radii and draw more radii. Notice each and every radius of a circle and mark all radii congruent. Draw new radii to important points on the circle, but don't draw a radius that goes to a point on the circle where nothing else is happening.
Use all the givens. Geometry book authors don't put irrelevant givens in proofs, so ask yourself why the author provided each given. Try putting each given down in the statement column and writing another statement that follows from that given, even if you don't know how it'll help you.
Check your ifthen logic.
For each reason, check that
All the ideas in the if clause appear in the statement column somewhere above the line you're checking.
The single idea in the then clause also appears in the statement column on the same line.
You can also use this strategy to figure out what reason to use in the first place.
Work backward. If you get stuck, jump to the end of the proof and work back toward the beginning. After looking at the prove conclusion, make a guess about the reason for that conclusion. Then use your ifthen logic to figure out the secondtolast statement (and so on).
Think like a computer. In a twocolumn proof, every single step in the chain of logic must be expressed, even if it's the most obvious thing in the world. Doing a proof is like communicating with a computer: The computer won't understand you unless every little thing is precisely spelled out.
Do something. Before you give up on a proof, put whatever you understand down on paper. It's quite remarkable how often putting something on paper triggers another idea, then another, and then another. Before you know it, you've finished the proof.
Subscribe to Blog via Email

Teaching Tessellations to Your Geometry Class

How to Teach Perimeter and Area of Similar Figures – in Jay Leno’s Garage

Christmas Math Worksheets

Introduction to Trigonometry

Ratios and Proportions – Bad Teacher!

How to Create a Jeopardy Game

Polygons in the Coordinate Plane – How to use Geogebra

5 Tips for New Teachers

8 Teacher Discounts you don’t want to miss this Summer

Your Students are Cheating with this Math App

Two Tips to Teach Volumes of Prisms and Cylinders

How to Setup and Use Google Classroom and Google Forms to Teach Geometry

Pi Day Top 5 for Geometry Teachers

Special Right Triangles – The Foundation of Everything Trig

How to use Google Forms and Word Clouds to Help your Students Master their Geometry Vocabulary

Interactive Geometry Teaching Techniques

The Magic Octagon – Understand congruence in terms of rigid motions

Attention Getters to Keep Your Geometry Class Locked in!

Teaching Strategies for your Inclusion Geometry Class without an Intervention Specialist

How to Teach the Properties of Quadrilaterals

Inequalities in One Triangle

Midsegments of Triangles

Classifying Polygons

Triangle Congruence by SSS and SAS

Pythagorean Theorem – NFL and Geometry

The Unit Circle – Hand Trick

How to make Geometry Interesting

How to Teach Circles Using the Common Core Standards?

Full Year of Geometry Lesson Plans

How a Rock Star Geometry Teacher Uses the iPad to Educate

Tessellation Project

Are you a Geometry Teacher with No Textbooks or Geometry Worksheets?

Geometry Games – Dance Dance Transversal

3 Ways to Make Your Life Easier as a Geometry Teacher Without More Geometry Worksheets

Parallel Lines and Transversals

Reasoning and Proof

How to Deal with a Class Clown – Classroom Management Strategies

Geometry Lessons  The Game Has Changed  Common Core Standards

Points Lines and Planes

How to Teach Dimensions – Geometry