1. 1.1 Points, Lines, and Planes

2. TermNamed byExample/Definition Point a capital letter -is a location, has no shape or size Line letters representing two points on the line OR a lowercase letter - no thickness or width - there is one line through any 2 points Plane capital script letter OR three letters on the plane -flat surface -one plane through any 3 points not on the same line

3. Collinear: points that lie on the same line Coplanar: points that lie on the same plane Space: boundless; 3D set of all points Intersection: where two or more sets of points cross

4. Two lines intersect at a _point_______ Two planes intersect at a __line_______

5. Example 1 Identify three collinear points and three non collinear points Collinear- __Z_, __Y__, __W__ Noncollinear- __X__, __Y__, __W__

6. Example 2 Name the plane shown in 5 different ways R U M S T plane __ M __, plane __RUT_, plane __SRU__, plane__TUR_, plane _STU_

7. Example 3 a)What is the intersection of plane HGC and plane AED? _HD___ b)Shade the plane that contains G, F, and D. c)Name a point that is coplanar with F and G. __H__ d)How many planes are there associated with this cube? __10__

8. 1.2 Linear Measure

9. TermNamed byExample Line Segment two endpoints -part of a line with two endpoints including all points between the endpoints Model: Betweenness of Points: Point M is between points P and Q if and only if P, Q, and M are collinear and __PM__ + __MQ___ = __PQ___. P M Q

10. Example 1 Find JL. Assume that the figure is not drawn to scale

11. Example 2 Find QR. Assume that the figure is not drawn to scale.

12. Example 3 If AB = 25, AN = 2x – 6, and NB = x + 7, find the value of x. Then find AN and NB. ABN 25 2x - 6 x + 7

13. Constructions!!! Congruent segments ( ): segments that have the same ____________.

15. 1.3 Distance and Midpoint

16. Distance between two points: _______________________________________ Distance on a number line: -4 0 5 Length of AB: a-b = ________________ Is the length of the segment from endpoint to endpoint -4 – 5= -9= 9

17. Distance on a Coordinate Plane: Length of MN: ___________ Length of NP: ____________ Use Pythagorean Theorem to find the length of MP a 2 +b 2 =c 2 4 3 M NP

18. Find the distance between two points using the Distance Formula: d =√ (x 2 -x 1 ) 2 +(y 2 -y 1 ) 2 Example 1: E(-5,6) and F(8,-4)

19. Example 2: J(4,3) and K(-3,-7)

20. Point halfway between the endpoints

21. Example 3: A(5,12) & B(-4,8) Example 4: C(-8,-2) & D(5,10)

22. Example 5: M is the midpoint of. Find RM, MT, and RT if RM = 5x + 9 and MT = 8x – 36.

23. Example 6: Find the coordinates of G if P(-5, 10) is the midpoint of EG and E has coordinates (-8,6).

24. Any segment line or plane that intersects a segment at the midpoint

25. 1.4 Angle Measure

26. TermNamed byExample Ray Opposite Ray Endpoint followed by point on the ray -part of a line, has one endpoint and goes in one direction Same as ray -two rays that have the same endpoint and are collinear Degree: ____________________________________________________________ Sides of an angle:__________________________________________________________ Angle: formed by two _________ with the same _____________, known as the _________. Unit used to measure angles Rays that make up angles raysendpoint vertex

27. ___________ __________ _______________________ ___< x < ____ x = ____ ____ < x < ____ x = ______ acute right obtuse straight 0o0o 90 o 180 o Congruent angles – have the same _________________ measure

28. Example 1: Name the angle at the in four ways. T S P ____________, _____________, _______________, ______________  TSP  PST  3  S (you may use the vertex to name an angle if there is only one angle)

29. Angle Addition Postulate If point B is in the interior of  AOC, then __________ + __________ = ___________ If AOC is a straight angle, then _________ + _____________ = __________ A B O C A O C B  AOB  BOC  AOC  AOB  BOC 180 o

30. Example 2: Use the diagram to answer the questions. A D B C

31. Example 3: Suppose KN bisects  JKL and the m  JKL = 9y + 15 and m  JKN = 5y + 2. Find m  JKL.

32. 1.5 Angle Relationships

33. ∠ 3 & ∠ 4 ∠ 3 & ∠ 2 ∠ 7 & ∠ 8 90 o 180 o right ∠ 5 & ∠ 6 ∠ 4 & ∠ 2

34. Example 1: Find the measures of two complementary angles if the measure of the larger angle is 12 more than twice the measure of the smaller angle.

35. Example 2: The measure of an angle’s supplement is 76 less than the measure of the angle. Find the measure of the angle and its supplement.

36. Example 3: Suppose m ∠ D = 3x – 12. Find x so that ∠ D is a right angle.

37. Example 4: Find the value of x and y. (y + 19) o (2x + 3) o (4x – 101) o

38. Constructions cont. Construct an angle congruent to the given angle: 1.Given angle P. Draw a ray with endpoint G.2. Place the compass at P and draw an arc that intersects both sides of the angle. Label the intersection M and N. 3. Using the same setting put the compass at G and draw an arc starting above the ray and ending at the ray. Label the intersection H. 4. Place the compass at N and adjust so the pencil is on M. Without changing the setting put the compass on H and draw an arc to intersect the arc from step 3. Label the point F. 5. Use a straightedge to draw GF. Resulting in ∠ MPN ≌ ∠ FGH P

39. Construct an angle bisector: 1. Put your compass at vertex A and 2. With the compass at Q draw an arc draw a large arc that intersects both in the interior of the angle. sides of ∠ A. Label the intersections Q and R. 3. Keep the same compass setting and put the compass on R and draw an arc that intersects the arc from step 2. Label the intersection T. 4. Draw AT Resulting in ∠ QAT ≌ ∠ RAT A

40. Construct a line perpendicular to line l and passing through point P on l : 1. Place the compass at P. Draw arcs on the 2. Set the compass to wider than right and left of P that intersect l. Label theAP. Put the compass at A and intersections A and B.draw an arc above line l. 3. Using the same setting put compass at B and draw an arc that intersects the previous arc. Label the intersection Q. 4. Using a straightedge draw QP. Resulting in AB QP when P is on line l P

41. Construct a line perpendicular to line k and passing through point P not on k. 1.Place the compass at P. Draw arcs that 2. Set the compass to wider than ½ CD. Intersect k in two different places. Label the Put the compass at C and draw an arc the intersections C and D. below line k. 3. Using the same setting put compass at D and draw an arc that intersects the previous arc. Label the intersection Q. 4. Using a straightedge draw PQ. Resulting in AB QP when P is not on line k. P