2. Geometry Basic Concepts Chapter 1 Unit 1 Coordinate Geometry and Basic Constructions

3. Section 1-7 Midpoint Formula

4. 1.7 Distance Formula Given (-3,-1) (-2,4) Find the distance!

5. Algebra Review Slope

6. Slope- Parallel and Perpendicular Parallel Lines have the same slope Perpendicular lines have the negative reciprocals

7. Suggested Practice for SOL G.3 Students need additional practice using slopes related to parallel or perpendicular lines. Line a passes through points with coordinates (-4, 5) and (2, -2). What is the slope of a line perpendicular to line a ? Slope of perpendicular line = 6

8. Find the coordinates of a point that lies on a line which passes through point P and is parallel to line c. Possible answers: (-10,0), (-7,-2), (-1,-6), (2,-8), (5,-10) Find the coordinates of a point that lies on a line which passes through point P and is perpendicular to line c. Possible answers: (-6,-7), (-2,-1), (0, 2), (2, 5), (4, 8) Suggested Practice for SOL G.3 Students need additional practice determining parallel and perpendicular lines on a coordinate grid. P c

9. Section 1.2 Points, Lines, and Planes PointA location in space Line a geometric figure made up infinitely many points; it extends endlessly in two directions Line Segment A part of a line; it has two endpoints RayA part of a line; it has one endpoint PlaneA flat surface; it has no thickness; it extends endlessly in all directions

10. 1.2 Name and Symbols Point A A Line AB or Line BA A B Line Segment AB or Line BA A B AB or BA

11. 1.2 Name and Symbols Ray BA ( Read “Ray BA”) B A BA Opposite Rays- are two rays consists of one endpoint and all the points of the line on one side of the endpoint. Plane ABC or Plane P

12. Section 1.2 2 lines intersect in a point 2 planes intersect in a line A line and a plane intersect in a point Through any three noncollinear points there is exactly one plane Collinear Points- points that lie on the same line. Coplanar -points and lines that lie in the same plane are coplanar. All the points of a line are coplanar

13. Section1.3 1.5 Ruler Postulate You can find the distance between two points in a number line by counting the number of spaces between the two points. The distance between points C and D is |c – d| or |d – c|. For example- Point C is at -1 Point D is at 5 -1 – 5 = -1+(-5) =-6 The absolute value of -6 is 6 |-6|=6 The length of the segment is the distance between the endpoints. The length of CD is 6. You write CD=6

14. 1.3 Congruent Line Segments

15. 1.3 Continue… Example Find the value of x in the diagram J K L M x+1 8 X+1 = 8 -1 -1 X= 7 Because JK is congruent to LM x is equal to 7.

16. Construction- A 1.3 congruent Line Segment G-4 A Video on constructions http://www.mathopenref.com/tocs/constructionstoc. html

17. 1.3 Midpoint of A Line Segment Midpoint-The point that divides a line segment into two congruent parts AM B Midpoint If AM =5 cm then MB =5 cm Any line, line segment, or ray that intersects a segment at its midpoint is called a bisector.

18. 1.3 Midpoint continue…. Line n bisects TR at point S. Find the length of TS. o TSR o TS= ½ TR o TR=10 in o TS= ½ 10 =5 o The length of TS is 5 in

19. 1.3 Constructions A bisector to a Line Segment Video on constructions http://www.mathopenref.com/tocs/constructionstoc. html

20. 1.3 Common Segment Theorem Common Segment Theorem If AB =CD, then AC=BD If AC=BD, then AB=CD ABC D Notice that in AD. BC is a common segment because it is a part of AC and part of BD. Find the length of AC if BC is 20.7 and CD 6.9. Since BD= BC +CD Then AC= 20.7 +6.9 AC=27.6

21. 1.3 Continue… Find the length of LM if KL =19.8 and JL=40.3 J K L M KM=JL and JK=LM KM= KL + LM 40.3=19.8 +LM -19.8 LM=20.5

22. Angle Vocabulary Sections 1.4 & 1.5 Angle A geometric figure formed by two rays with a common endpoint ProtractorA tool used to measure angles Acute angle An angle that is greater than 0 degrees and less than 90 degrees Right angleAn angle that is equal to 90 degrees Obtuse angle An angle that is greater than 90 degrees but less than 180 degrees Straight angleAn angle that is equal to 180 degrees

23. Continue… Adjacent angles Two angles that have a common vertex and a common ray Complementary angles A pair of angles whose measures have a sum of 90 degrees Supplementary angles A pair of angles whose measures have a sum of 180 degrees Congruent anglesAngles that have the same measure Vertical anglesAngles formed by intersecting lines Angles bisectorA ray that divides angle into congruent angles

24. Section 1.4 Measuring Angles Angle-A geometric figure formed by two rays with a common endpoint. The endpoint is called the vertex of the angle. You can use the angle symbol The angle on the left is ABC or CBA. You can also use thvertex alone B.

25. Angles Continue…

26. Measuring Angles Continue…. Protractor -A tool used to measure angles. An angle is measured in degrees. The symbol for degree is To find a measure of angle you place the center of the protractor’s straight edge on the vertex. One ray must pass through 0 degrees on the protractor. Use the scale that reads O degrees on the first ray. Read the number of degrees where the second ray crosses the protractor.

27. Continue….

28. 1.7 Protractor Postulate The protractor postulate allows you to find the measure of an angle by finding the absolute value difference of real numbers. See page 28

29. Congruent Angles

30. Angle Addition Postulate See page 30 If point B is in the interior of AOC then m AOB + m BOC = m AOC

31. Constructions A congruent Angle Video on constructions http://www.mathopenref.com/tocs/constructionstoc. html

32. Vertical Angle Vertical angles -Angles formed by intersecting lines

33. CONSTRUCTION An Angle Bisector Video on constructions http://www.mathopenref.com/tocs/constructionstoc. html

34. Common Angles Common Angle Theorem – Point D and E are in the interior of angle ABC. If m ABD =m EBC, then m ABE =m DBC. If m ABE= m DBC, then m ABD = m EBC.

35. 1.6 Basic Constructions http://www.mathopenref.com/tocs/constructionsto c.html http://www.mathopenref.com/tocs/constructionsto c.html Constructing Congruent Segments Constructing Congruent Angles Constructing the Perpendicular Bisector Constructing Angle Bisector

36. Review Classifying Polygons

37. 1.8 Area, Circumference, and Perimeter

38. 1.1 SectionNets and Drawings for Visualizing Geometry Net is a two-dimensional diagram that you can fold to form a three dimensional figure. Isometric drawing shows a corner view of a three – dimensional figure. It allows you to see the top, front and side of a figure. See page 6 Orthographic drawing- is another way to represent a three-dimensional figure. An orthographic drawing shows three separate views a top view, front view, and a right side view. See page 6