FINAL EXAM REVIEW Chapters 1-2 Key Concepts

Chapter 1 Vocabulary equidistantpointlineplanecollinearcoplanarintersectionsegmentraydistance angleacuteobtuse right angle postulatetheorem

Segment Addition Postulate If B is between A and C, then… If B is between A and C, then… AB + BC = AC. AB + BC = AC. A. C. B.

Angle Addition Postulate If Point B lies in the interior of AOC, then m AOB + m BOC = m AOC

Angle Addition Postulate PART 2 If Point B lies in the interior of straight AOC, then m AOB + m BOC = 180

Postulate 6  Through any two points there is exactly one line. B. A.

Postulate 7  Through any three noncollinear points there is exactly one plane.. C. B. A

Postulate 8  If two points are in a plane, then the line that contains the points is in the plane. A. B.

Postulate 9  If two planes intersect, then their intersection is a line. A. B.

Theorem 1.1  If two lines intersect, then they intersect in exactly one point. A.

Theorem 1.2  Through a line and a point not in the line, there is exactly one plane. A.

Theorem 1.3  If two lines intersect, then exactly one plane contains the lines.

Chapter 2 Vocabulary if-then statement hypothesisconversemidpointcongruent complementary <‘s supplementary <‘s adjacent <‘s perpendicularproof POE’s and POC’s ► addition ► subtraction ► multipl./division ► distributive ► reflexive ► symmetric ► transitive

Midpoint Theorem IIIIf M is the midpoint of, then AM = (1/2)AB and MB = (1/2)AB How is this different from the midpoint defn.? Key: The midpoint theorem uses ½. A.A. M.M. B.B.

Angle Bisector Theorem  If BX is the bisector of, then How is this different from the angle bisector defn.? Key: The theorem uses ½..C.C B.. X. A. A

Theorem Vertical angles are congruent. Given:Prove: 12 3 ‘s‘s 1 and 2 are vertical Think:What do you know about the sum of the measure of supplementary 7 ‘s‘s 1 and 3 ? 7 ‘s‘s 2 and 3 ? The sum = 180

If two lines are perpendicular, then they form congruent adjacent angles. lines adj. If two lines form congruent adjacent angles, then the lines are perpendicular. adj. lines Example If, MN JK Because adj, form lines Perpendicular Line Theorems. M. N J.J. K.K

Theorem If the exterior sides of two adjacent angles are perpendicular, then the angles are complementary. Ext. sides of 2 adj. comp. If OA OC, then… are complementary. O..C.C B. 1 2 A.

Theorem: Supplements of Congruent ‘s Supplements of congruent angles (or the same angle) are congruent If 1 and 3 are 7 7 Then 2 and 4 are also 7 7

Theorem: Complements of Congruent ‘s Complements of congruent angles (or the same angle) are congruent If 1 and 3 are 7 7 Then 2 and 4 are also 7 7

Homework ► pg all