Would You Rather Listen to the Lesson?

Planning a Proof in Geometry is one of the most nerve racking subjects in the course. For the average student who will never be a math major or professor, being able to write a mathematical proof from scratch is not all that important. All of the standardized test only require that the students be able to fill in missing pieces to proofs that are already assembled for them. However, the most important thing these non math major kids will learn in your geometry course is how to do a proof. Allow me to explain...
Our Responsibility as Teachers
We have the responsibility of not only teaching our students our content area but also how to grow as an individual mentally, socially, and so on. Planning a proof is more about learning to reason and logically think through a process, to draw a conclusion, to create a plan than it is about the algebra or geometry behind the proof.
Why Proofs Are Difficult for Students
Now, let's discuss why proofs are so difficult for students. First, the way we are taught to teach proofs is to cram a bunch of theorems and postulates into a short time frame in which they are supposed to master, some of which were even based off of content they learned in the previous chapter on angles. So the students are already lost and uncomfortable with the material they are supposed to be using as facts and reasons for the proofs, which they do not know how to construct yet either!
It's Not the Process!
What we have to understand as their teacher is that it is not the actual process of planning a proof that is the issue. It is there prior knowledge of the topics they are trying to construct the proofs on. Try this, take a day and work only on one topic. For example, vertical angles. Teach them and lead a discussion on vertical angles. Do enough examples so that they are all comfortable with the topic. Then at the end of class lead them through planning a proof (a two column proof) that shows that vertical angles are congruent. When you do this don't tell them they are planning a proof, let them walk you through it by you asking leading questions. Then once the proof is over let them know they as a class just created their first proof.
Build Confidence First
They need to start with that confidence. Instead of teaching a chapter on proofs mix them in with the topics as you teach them. Meaning when you teach triangles go through the proofs with each triangle, when you teach complementary and supplementary go through each of the proofs with them. The problem is when we teach just a unit on proofs we are also asking them to recall things they learned long ago. Not that this is a bad thing but it does destroy the confidence of the students who naturally struggle with math.
Rework your lessons so that they see proofs throughout their entire geometry class. If you don't have the time to rework your lesson plans you can download ours by CLICKING HERE. The stress, time, and frustration this will save you is well worth the effort.
Here are your Free Resources for this Lesson!
Planning a Proof Worksheet, Word Docs & PowerPoints
To gain access to our editable content Join the Geometry Teacher Community!
Here you will find hundreds of lessons, a community of teachers for support, and materials that are always up to date with the latest standards. The lessons in this unit include...
Unit 2  Reasoning and Proof
21 Inductive and Deductive Reasoning
25 Theorems about Angles and Perpendicular Lines
26 Planning a Proof
Planning a Proof  PDFs
26 Assignment Student Edition  Planning a Proof ( FREE )
26 Assignment Teacher Edition  Planning a Proof (Members Only)
26 Bell Work Student Edition  Planning a Proof ( FREE )
26 Bell Work Teacher Edition  Planning a Proof (Members Only)
26 Exit Quiz Student Edition Planning a Proof ( FREE )
26 Exit Quiz Teacher Edition  Planning a Proof (Members Only)
26 Guided Notes Student Edition  Planning a Proof ( FREE )
26 Guided Notes Teacher Edition  Planning a Proof (Members Only)
26 Lesson Plan  Planning a Proof (Members Only)
26 Online Activities  Planning a Proof (Members Only)
26 Slide Show  Planning a Proof ( FREE )
Want access to the rest of the materials on Planning a Proof?
To download the rest of the materials for this lesson and get updates via email when new lessons come out simply click the image below to Get All of Our Lessons!
Below is an excerpt from Proofs for Dummies
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.

Proofs with Uno Cards

Valentine’s Day Math Activity – Classifying Quadrilaterals

Christmas Math Worksheets

Thanksgiving Worksheet for Geometry – Happy Turkey Day!

Halloween Geometry Activities High School

How to Teach Classifying Polygons

Points Lines and Planes

Tessellation Project

The Unit Circle – Hand Trick

Introduction to Trigonometry

Pi Day Top 5 for Geometry Teachers

Polygons in the Coordinate Plane – How to use Geogebra

Teaching Tessellations to Your Geometry Class

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

Reasoning and Proof

Geometry Games – Dance Dance Transversal

Midsegments of Triangles

Triangle Congruence by SSS and SAS

Pythagorean Theorem – NFL and Geometry

Inequalities in One Triangle

Parallel Lines Cut by a Transversal – Colorful Flip Book Notes

Measuring Angles PuttPutt Course Design Project

How to Teach Tangent Lines – Graphic Organizer

Segment Addition Postulate

Two Tips to Teach Volumes of Prisms and Cylinders

Parallel Lines and Transversals

Nets and Drawings for Visualizing Geometry – Geometry Nets Project

Ratios and Proportions – Bad Teacher!

Hybrid Flipped Classroom Model

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

How to Create a Jeopardy Game

5 Tips for New Teachers

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

Your Students are Cheating with this Math App

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

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

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

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

How to Deal with a Class Clown – Classroom Management Strategies

Geometry Lessons  The Game Has Changed  Common Core Standards

Teaching Dimensions with Super Mario – Geometry

Lesson for the First Day of Geometry Class