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Perpendicularity can not be assumed. If lines, segments, or rays intersect to form right angles then they are perpendicular. 

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Perpendicularity can not be assumed. If lines, segments, or rays intersect to form right angles then they are perpendicular. 

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If 2 angles sum to 90 degrees then they are complementary

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If 2 angles sum to 90 degrees then they are complementary

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If 2 angles sum to 180 degrees then they are  supplementary

If you add adjacent in either of those proofs you can claim to be right or straight angles

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If two angles are supp or comp to the same angle then they are congruent. 

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If two angles are supp or comp to the same angle then they are congruent. 

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If two angles are supp or comp to congruent angles then they are congruent.

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If congruent segments or angles are added to congruent segments or angles then the sums are congruent. 

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If congruent segments or angles are added to congruent segments or angles then the sums are congruent. 

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REFLEXIVE PROP
Angles are congruent to themselves

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If congruent segments or angles are subtracted from congruent segments or angles then the differences are congruent.

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Knowing that both angles/ segs are bisected or trisected lets you know that the angle is being doubled or tripled.

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Knowing that both angles/ segs are bisected or trisected lets you know that the angle is being doubled or tripled.

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If angles or segs are congruent, then their like doubles and triples are congruent. 

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If angles or segs are congruent, then their like doubles and triples are congruent. 

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If congruent segs are bisected then their like halves or thirds are congruent.

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If congruent segs are bisected then their like halves or thirds are congruent.

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Substitution is used to plug in for values.  Use the transitive property to connect a chain of congruence. 

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Substitution is used to plug in for values.  Use the transitive property to connect a chain of congruence. 

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TRANSITIVE PROPERTY
If angles or segs are congruent to the same angle or seg then they are congruent.

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Opposite rays are two collinear rays that have a common endpoint and extend in different directions. 

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Opposite rays are two collinear rays that have a common endpoint and extend in different directions. 

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Two angles are vertical angles if the rays forming the sides of one and the rays forming the sides of the other are opposite rays. 

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Two angles are vertical angles if the rays forming the sides of one and the rays forming the sides of the other are opposite rays. 

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I have developed a better understanding of different theorems by reviewing my notes, and doing extra problems. I also created a study guide with all the theorems used so far. Overall I improved by correcting and noting the mistakes I made on the quiz, and noting what I can do to prevent them. It helped me to make a list of things to remember, so I can focus on studying things I have trouble with instead of things I already know. I feel very confident for the upcoming test because of the work I have done to prepare. 

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I have developed a better understanding of different theorems by reviewing my notes, and doing extra problems. I also created a study guide with all the theorems used so far. Overall I improved by correcting and noting the mistakes I made on the quiz, and noting what I can do to prevent them. It helped me to make a list of things to remember, so I can focus on studying things I have trouble with instead of things I already know. I feel very confident for the upcoming test because of the work I have done to prepare. 

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Five Step Procedure is how we write complicated proofs. 

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Five Step Procedure is how we write complicated proofs. 