GEOMETRY – VALID PROOF REASONS

I will continually update this entry as we get more and more reasons that we can justify using in proofs.  The newer reasons are bolded.

GEOMETRY -  VALID PROOF REASONS

¨      TRANSITIVE PROPERTY

¨      SUBSTITUTION PROPERTY

¨      GIVEN

¨      SIMPLIFY/COMBINE LIKE TERMS

¨      ADDITION POE

¨      SUBTRACTION POE

¨      MULTIPLICATION POE

¨      DIVISION POE

¨      SYMMETRIC PROPERTY

¨      DISTRIBUTIVE PROPERTY

¨      DEFINITION OF COMPLEMENTARY

¨      DEFINITION OF SUPPLEMENTARY

¨      DEFINITION OF CONGRUENCY

¨      DEFINITION OF SEGMENT BISECTOR

¨      DEFINITION OF MIDPOINT

¨      DEFINITION OF ANGLE BISECTOR

¨      REFLEXIVE PROPERTY

¨      ANGLE ADDITION POSTULATE

¨      SEGMENT ADDITION POSTULATE

¨      ALL RIGHT ANGLES ARE CONGRUENT.

¨      TWO PERPENDICULAR LINES FORM FOUR RIGHT ANGLES.

¨      DEFINITION OF RIGHT ANGLES

¨      DEFINITION OF PERPENDICULAR

¨      VERTICAL ANGLES ARE CONGRUENT.

¨      SUPPLEMENTS OF THE SAME ANGLE ARE CONGRUENT.

¨      COMPLEMENTS OF THE SAME ANGLE ARE CONGRUENT.

¨      SUPPLEMENTS OF CONGRUENT ANGLES ARE CONGRUENT.

¨      COMPLEMENTS OF CONGRUENT ANGLES ARE CONGRUENT.

¨      180-360 POSTULATE

¨      IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN:

1.     ALTERNATE INTERIOR ANGLES ARE CONGRUENT.

2.     ALTERNATE EXTERIOR ANGLES ARE CONGRUENT.

3.     CORRESPONDING ANGLES ARE CONGRUENT.

4.     SAME-SIDE INTERIOR ANGLES ARE CONGRUENT.

¨      TWO LINES CUT BY A TRANSVERSAL ARE PARALLEL IF:

1.     ALTERNATE INTERIOR ANGLES ARE CONGRUENT.

2.     ALTERNATE EXTERIOR ANGLES ARE CONGRUENT.

3.     CORRESPONDING ANGLES ARE CONGRUENT.

4.     SAME-SIDE INTERIOR ANGLES ARE SUPPLEMENTARY.

¨      IN A PLANE, IF TWO LINES ARE PERPENDICULAR TO THE SAME LINE, THEN THEY ARE PARALLEL.

¨   THE TRIANGLE SUM THEOREM – THE SUM OF THE MEASURES OF THE ANGLES IN A TRIANGLE IS 180 DEGREES.

¨   THIRD ANGLES THEOREM – IF TWO ANGLES IN A TRIANGLE ARE CONGRUENT TO TWO ANGLES IN A 2ND TRIANGLE, THEN THE THIRD ANGLES ARE ALSO CONGRUENT. 

 

 

 

 

 

 

 

About these ads

One Response to GEOMETRY – VALID PROOF REASONS

  1. Lisa Brooks says:

    I am a new Geometry teacher, and I am struggling with the idea of giving my students a list of the Reasons for proofs. These particular students want everything given to them, and I want them to work for what they get. What are your thoughts on this?

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

%d bloggers like this: