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Opening Activity

Opening Activity. Give an example of a point , line and plane that can be found in the classroom. Geometry Online Textbook. 1.1 Points, Lines, & Planes. Foldable Activity. What is a definition?. Known words used to describe a new word Undefined terms – not formally defined

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Opening Activity

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  1. Opening Activity • Give an example of a point, line and planethat can be found in the classroom.

  2. Geometry Online Textbook 1.1 Points, Lines, & Planes

  3. Foldable Activity

  4. What is a definition? • Known words used to describe a new word Undefined terms – not formally defined There are 3 in geometry. Point Line Plane

  5. Point

  6. Line Can be called: Line l Line AB or AB Line BA or BA l A B

  7. Plane Can be named: Plane W Plane ABC, plane BCA, plane CBA, etc. A W C B

  8. More Definitions • Collinear points – points that lie on the same line • Coplanar points – points that lie on the same plane • Space – a boundless, three-dimensional set of all points. Space can contain lines and planes.

  9. IDENTIFY AND NAME THE FOLLOWING: • POINT • LINE • PLANE • COLLINEAR POINTS • NONCOLLINEAR POINTS • COPLANAR POINTS • NONCOPLANAR POINTS

  10. Practice

  11. AssignmentHandout

  12. Warm up Practice

  13. Geometry Online Textbook 1.2 Linear Measures User Name: GEOVA05 Password: crAju4re

  14. Line Segment (or segment) • A section of a line that has 2 endpoints • Named by its endpoints. AB or BA • The length or measure of AB is written as AB. A B

  15. Example: Find the length of AB using the ruler. A B

  16. BETWEENNESS OF POINTS

  17. PRACTICE Find the value of the variable and LM if L is between N and M. • NL = 5x, LM = 3x, and NL = 15 • NL = 6x – 5, LM = 2x + 3, and NM = 30

  18. CONGRUENT SEGMENTS • Two segments having the same measure are congruent. • is read is congruent to. (Red slashes indicate t he segments are congruent.) 2 cm 2 cm

  19. Independent Practice • Handout • Homework Page 17 22 – 39 all

  20. Geometry Online Textbook 1.3 DISTANCE AND MIDPOINTS User Name: GEOVA05 Password: crAju4re

  21. Warm up Practice

  22. DISTANCE BETWEEN TWO POINTS Number line Coordinate Plane • PQ = | b – a | or | a – b | • Example Find the distance between the two points -5 and 1. • The distance between d between two points with coordinates (x2 - x1) and (y2 – y1) is given by d = √ (x2 – x1)2 + (y2 – y1)2 • Example Find the distance between R(5.1) and S(-3,-3).

  23. Midpoint of a Segment • Used for finding the coordinates of the midpoint of a segment in a coordinate plane. • If the endpoints are (x1,y1) & (x2,y2), then

  24. Ex: Find the midpoint of SP if S(-3,-5) & P(5,11

  25. Ex: The midpoint of AB is M(2,4). One endpoint is A(-1,7). Find the coordinates of B.

  26. Independent Practice • Handout • Homework Page 25-26 13-18 all; 23-28 all; 31 - 44 all • Quiz next block on Sections 1-1 to 1-3 • You must know the Distance and Midpoint Formulas • Study!!!!

  27. Geometry Online Textbook 1.4 Angle Measures User Name: GEOVA05 Password: crAju4re

  28. Warm up Practice

  29. Angle symbol: • 2 rays that share the same endpoint (or initial point) Sides – the rays XY & XZ Vertex – the common endpoint; X Y X 5 Z Named <YXZ, <ZXY (vertex is always in the middle), or <X (if it’s the only <X in the diagram). Angles can also be named by a #. (<5)

  30. There are 3 different <B’s in this diagram; therefore, none of them should be called <B. A <B ? D B C

  31. Angle Measurement • m<A means the “measure of <A” • Measure angles with a protractor. • Units of angle measurement are degrees (o). • Angles with the same measure are congruent angles. • If m<A = m<B, then <A  <B.

  32. B is ___________ C is ___________ D is ___________ Interior or Exterior? in the interior in the exterior on the < B C D A

  33. Acute angle – Right angle – Obtuse angle – Straight angle – Measures between 0o & 90o Measures exactly 90o Measures between 90o & 180o Measures exactly 180o Types of Angles

  34. Ray • Piece of a line with only one endpoint (initial point) and continues forever in the other direction • Named by the endpoint and a second point named on the ray. (name MUST begin with the endpoint!) AB A B

  35. Opposite Rays • 2 rays that share a common initial point and face opposite directions. • QP and QS are opposite rays. P Q S

  36. Congruent Angles Angles that have the same measure are congruent angles. Arcs on the figure also indicate which angles are congruent.

  37. Practice

  38. Example: 6 volunteers please! • Draw & label points A & B. • Draw & label points C & D. • Draw AB. • Draw BC. • Draw AC. • Draw DA.

  39. More Definitions • Intersect – 2 or more figures intersect if they have one or more points in common. • Intersection – all points or sets of points the figures have in common • What is the intersection of: AB & DA BC & AC BC & BC

  40. When 2 planes intersect, their intersection is a line.

  41. Assignment

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