Sections 2.3 & 2.4Sections 2.3 & 2.4

2.3 Drawing Conclusions2.3 Drawing Conclusions

&&

2.4 Supplement Theorem2.4 Supplement Theorem

Complement TheoremComplement Theorem

Procedure for Drawing Procedure for Drawing ConclusionsConclusions

Memorize theorems, definitions, and Memorize theorems, definitions, and postulatespostulates

Look for key words and symbols in the given Look for key words and symbols in the given informationinformation

Think of all the theorems, definitions, and Think of all the theorems, definitions, and postulates that involve those keyspostulates that involve those keys

Decide which theorem, definition, or postulate Decide which theorem, definition, or postulate allows you to draw a conclusionallows you to draw a conclusion

Draw a conclusion, and give a reason to justify Draw a conclusion, and give a reason to justify the conclusion. Be certain that you have not the conclusion. Be certain that you have not used the reverse of the correct reason.used the reverse of the correct reason.

Vertical Angles Vertical Angles ConjectureConjecture

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 The Bow TieTie” View of

a Pair of

Vertical Angles

What conclusion might you venture?

Linear Pair ConjectureLinear Pair Conjecture

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

Parallelogram ConjectureParallelogram Conjecture

What conclusion might you venture?

Parallelogram ConjectureParallelogram Conjecture

What conclusion might you venture?

ExampleExample

C

AB

D

Given: bisects CAD

Conclusion?

The key word is bisects

The key symbols are and

The definition of bisector (of an angle) contains those keys

An appropriate conclusion is that CAB DAB

AB

55555555555555

bisects CADAB 55555555555555

Statement Statement ReasonReason

GivenGiven

If a ray bisects an If a ray bisects an angle then it angle then it

divides the angle divides the angle into two congruent into two congruent

anglesangles

CAB DAB

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