Sections 2.3 & Drawing Conclusions & 2.4 Supplement Theorem Complement Theorem Complement Theorem

Procedure for Drawing Conclusions Memorize theorems, definitions, and postulates Memorize theorems, definitions, and postulates Look for key words and symbols in the given information Look for key words and symbols in the given information Think of all the theorems, definitions, and postulates that involve those keys Think of all the theorems, definitions, and postulates that involve those keys Decide which theorem, definition, or postulate allows you to draw a conclusion Decide which theorem, definition, or postulate allows you to draw a conclusion Draw a conclusion, and give a reason to justify the conclusion. Be certain that you have not used the reverse of the correct reason. Draw a conclusion, and give a reason to justify the conclusion. Be certain that you have not used the reverse of the correct reason.

Vertical Angles Conjecture Vertical angles are non-adjacent angles formed by a pair of intersecting lines. You can think of them as the opposite angles that appear in the "bow-tie" formed when two lines intersect

The Bow Tie “The Bow Tie” View of a Pair of Vertical Angles What conclusion might you venture?

Linear Pair Conjecture Above angles <A and <B are a linear pair. What conclusion might you venture?

Parallelogram Conjecture What conclusion might you venture?

Parallelogram Conjecture What conclusion might you venture?

ExampleStatementReasonGiven If a ray bisects an angle then it divides the angle into two congruent angles

Theorem 4: If angles are supplementary to the same angle, then they are congruent. Theorem 5: If angles are supplementary to the congruent angles, then they are congruent. ST The Supplement Theorem(s) Abbreviated: ST 2.4 Supplement Theorem & Complement Theorem

Theorem 6: If angles are complementary to the same angle, then they are congruent. Theorem 7: If angles are complementary to congruent angles, then they are congruent. CT The Complement Theorem(s) Abbreviated: CT