Transcript Slide 1
1.2 Geometry Definitions Geometry Symbols m Definitions 1. Collinear- ________________________________ 2. Non-Collinear- ____________________________ 3. Coplanar- ________________________________ 4. Distance- ________________________________ __________________________________________ -11 23 5. Segment- _____________________________ _______________________________________ 6. Ray- _________________________________ Opp Ray- _____________________________ _______________________________________ 7. Congruent- ___________________________ 8. Midpoint- _____________________________ 9. Bisector- _____________________________________ -____________________________________ -____________________________________ 10. Angle- _____________________________________ Acute: _____________________________ Obtuse: ____________________________ Right: ______________________________ Straight: ____________________________ 11. Vertical Angles- ____________________________ _______________________________________________ 12. Adjacent Angles: ___________________________ _______________________________________________ 1 2 13. Supplementary- ________________________ 14. Complementary- _______________________ 15. Perpendicular- _____________________________ 16. Plane- __________________________________ _____________________________________________ Note: ___________________________________ _________________________________________ _________________________________________ _________________________________________ Examples 1. There is a Right angle at each corner of PRST. a) if angle TPO=60: RPO= ? b) if angle PTO=70: STO= ? c) if angle TOP=50: POR= ? T S O P R 1. If CBD CAB= ? DBE and BD bisects C D X+10 X+5 A 60 B E CBE find 3. 1 2; m 1 x 14; m 2 y 3 Solve for y in terms of x. 2 1 4. m ABD 3x; m DBC x; Find m ABD D A B C 5. m FGJ 3x 5; m JGH x 27; GJ bisects FGH Find m FGJ J F G H 6. m ABC 90; m 1 2 x 10; m 2=x+20; m 3=3x Find x C 1 B 2 3 A 1.3 and 1.4 Segment and Angle Addition Postulates Define First: •Definition: _________________________ •Postulate: ___________________________________ ___________________________________ •Theorem___________________________________ ___________________________________ Segment Addition Postulate _______________________________________________ _______________________________________________ _______________________________________________ A B If B is between A and C then: C Angle Addition Postulate _______________________________________________ _______________________________________________ C B B O A A O If B lies on the interior of angle AOC then: or C Examples B is between A and C, with AB=x and BC=2x+5. If AC=35: Find x and BC A B C AL bisects KAT .Find the value of x. K L 2 3 M 1. m 1 3x; m 2 4 x 15 2. m 2 x 6; m 3 4 x 1 A T 1.5 Postulates &Theorems You do not need to memorize the numbers, just know what the theorem or postulate says! Postulate 5 •______________________________________ • •______________________________________ • _____________________________________ Postualte 6: • _______________________________________ ________________________________________ Postualte 7: • ________________________________________ __________________________________________ __________________________________________ Postualte 8: • _________________________________________ __________________________________________ Postualte 9: • _____________________________________ ______________________________________ Theorem 1.1: • ______________________________________ _______________________________________ Theorem 1.2: • _____________________________________ ______________________________________ Theorem 1.3: • ______________________________________ _______________________________________ _______________________________________ Theorem 1.4: • _______________________________________ ________________________________________ ________________________________________ ________________________________________ •Is TW on plane m? x •Are TSW coplanar? •Are RWY coplanar? T R S o W •Where does XY intersect plane m? How many lines contain point T and S? How many planes contain T, S and X? m y •Where do planes R & S intersect? A R B s Name 3 lines that intersect E? S Name 2 planes that intersect at FG? R Name 2 planes that don’t intersect? H E F G D C Are points RSGC coplanar? A B