Chapter 1: Tools of Geometry

1. Chapter 1: Tools of Geometry Lesson 1: Points, Lines and Planes

2. Definitions • Point- represents a location • Line- made up of points and has no thickness or width, extends infinitely at both ends (cannot be measured) • Collinear- points on the same line • Plane- flat surface made from points that has no depth and extends in all directions infinitely • Coplanar- points or lines on the same plane • Space- boundless, 3-D set of all points that contains lines and planes

3. Chapter 1 Foldable • Step 1- fold the construction paper in half both by width and length (hamburger and hotdog) • Step 2- Unfold the paper and hold width wise, fold in the ends until they meet at the center crease • Step 3- Cut the folded flaps along the crease so that there are now 4 flaps

4. Upper Left flap- Lesson 1.1 Points, Lines and Planes • Label the outside of the flap with the lesson number and title. • Inside the flap create a grid with 7 columns and 4 rows.

5. Copy the notes into the foldable, then draw and label your own examples based on the information in the chart. P n B A X Y Z S

6. A. Use the figure to name a line containing point K. B. Use the figure to name a plane containing point L. C. Use the figure to name the plane two different ways.

7. A. Name the geometric shape modeled by a 10  12 patio. B. Name the geometric shape modeled by a water glass on a table. C. Name the geometric shape modeled by a colored dot on a map used to mark the location of a city. D. Name the geometric shape modeled by the ceiling of your classroom.

9. A. How many planes appear in this figure? B. Name three points that are collinear. C. Are points A, B, C, and D coplanar? Explain.

10. Chapter 1: Tools of Geometry 1.2 Linear Measure

11. Definitions • Line segment- part of a line that has two endpoints and can be measured(named by the letters marking the endpoints) • Congruent- same shape and size (segments that have the same measure)

12. A.Find LM. B. Find XZ.

13. C. Find x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.

14. Find SE.

15. Find a if AB = 4a + 10, BC = 3a – 5, and AC = 19.

16. Chapter 1: Tools of Geometry Lesson 3: Distance and Midpoint

17. Definitions • Midpoint- the point on a segment that divides the segment into two congruent segments • Segment bisector- any line, segment or plane that intersects a segment at its midpoint

18. Distance Formula- used to find the length of a segment. ex: Find the distance between A (5,1) and B (-3, -3). *on a number line- subtract the endpoint values Midpoint Formula- used to find the point half way down a segment ex: Find the midpoint of JK if J(-1,2) and K(6, 1) * on a number line- add the endpoint values and divide by 2 Distance and Midpoint

19. Use the number line to find the midpoint and the measure of AX.

20. Find the midpoint and distance between E(–4, 1) and F(3, –1).

21. Find the distance and midpoint of AM

22. Find the coordinates ofRifN (8, –3) is the midpointofRSandShas coordinates (–1, 5).

24. Find LM. Assume that the figure is not drawn to scale.

25. Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.

26. Find the value of n and WX if W is between X and Y, WX = 6n – 10, XY = 17, and WY = 3n.

27. Chapter 1: Tools of Geometry Lesson 4: Angle Measure

28. Definitions • Degree- the unit of measurement for an angle • Ray- a part of a line which has one endpoint and one end that extends infinitely (name with the endpoint first and then any other point on the ray) • Opposite rays- two rays that share an endpoint and extend in opposite directions (together they make a line) • Angle- formed by two non-collinear rays that have a common endpoint • Sides of an angle- rays • Vertex- the common endpoint of the rays of an angle • Angle Bisector- a ray or line that divides an angle into two congruent angles

29. Naming and Classifying Angles A Angle: -B is the vertex -ray BA and ray BC are the sides( BA and BC ) -Angle names: ABC, CBA B, 4 -Angle bisector : makes 2 congruent angles 4 B C

30. C. A. Name all angles that have B as a vertex. B.Name the sides of5.

31. A. Measure TYV and classify it as right, acute, or obtuse. B.Ray YT bisects angle SYU. Angle TYS = 2x-24, angle UYT = x+16. Find x and the measure of angle SYU.

32. Chapter 1: Tools of Geometry Lesson 5: Angle Relationships

33. Definitions • Adjacent angles: two angles that lie in the same plane, have a common vertex and a common side, but no common interior points • Vertical angles: two nonadjacent angles formed by two intersecting lines • Linear pair: a pair of adjacent angles with non-common sides that are opposite rays • Complementary angles: two angles with measures that add up to 90 • Supplementary angles: two angels with measures that add up to 180 • Perpendicular ( ): lines, segments or rays that form right angles

34. Angle Relationship examples D M A O C B L N E D B A 72 18 C R U S V 40 140 T

35. A. Name two adjacent angles whose sum is less than 90. B. Name two acute vertical angles.

36. Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle.

37. A. Name an angle supplementary to BEC. B. Name a linear pair whose vertex is E. C. Name two acute vertical angles.

38. Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other.

39. The supplement of A measures 140 degrees. What is the measure of the complement of A?

40. ALGEBRA Find x and y so thatKO and HM are perpendicular.