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find rays with same start pont and different directions

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use knowledge that rays are going up or down not side to side

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use this property to have two congruent angles or segs trade places

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use this two find the difference of two angles or segments and use it in proofs.

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use this to use the sum of two angles or segments in a proof

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prove angles are congruent by means of four new theorems

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prove angles are congruent by means of four new theorems

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we learn about 4 new theorems, addition subtraction, multiplication, and division

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follow a five step procedure to draw logical conclusions.

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follow a five step procedure to draw logical conclusions.

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You use this when trying to prove a complex answer that cant be explained by a 2 step procedure.

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recognize complementary and supplementary angles

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recognize complementary and supplementary angles

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this is used when finding the sum of two angles that are 90 degrees or 180.

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Understand the need for perpendicularity

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Understand the need for perpendicularity

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You need this to conclude proofs we do in this chapter

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Recognize the need for conclusion in proofs

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Recognize the need for conclusion in proofs

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You need this because it makes your proof valid.