Exit Level

1. Exit Level TAKS Preparation Unit Objective 7

2. Nets and 3-D figures • When given a net, try to imagine what it would look like when folded up. • Here are some common nets: 7, Gb1B

3. Cubes and Rectangular Prisms • The net of a cube is made entirely of squares • The net of a rectangular prism contains rectangles 7, Gb1B

4. Pyramids • The net of a triangular pyramid has a triangle for its base • The net of a square pyramid has a square for its base 7, Gb1B

5. Prisms with other bases • A Pentagonal Prism has a pentagon for its bases • A Hexagonal Prism has a hexagon for its bases 7, Gb1B

6. Use your imagination! • Example: The net below can be folded to form a cube. Which cube could be formed from this net? A. B. C. D. 7, Gb1B

7. 3 2 1 2 1 1 Views of 3-D Solids • You must be able to imagine a 3-D solid from every angle Left Front Left Top Right Right Front 7, Gd1C

8. Views of 3-D Solids, cont… • Example: The 3-dimensional figure shown below represents a structure that Jessica built with 11 cubes. Which of the following best represents the top view of Jessica’s structure? A. B. C. D. Front Right 7, Gd1C

9. Quadrilaterals (four sided figures) • Rectangle • Square • Rhombus • Trapezoid • Parallelogram Isosceles Trapezoid 7, Gd2A

10. Other Important Shapes • Pentagon – five sided • Hexagon – six sided • Regular – perfect shape • All sides congruent • All angles congruent 7, Gd2A

11. The Coordinate Plane y-axis (x, y) (2, 5) An ordered pair (point) is graphed by using the x to move right or left and the y to move up or down Quadrant II Quadrant I (-3, -5) x-axis Quadrant III Quadrant IV 7, Gd2A

12. Key Geometry Terms • Collinear – points that lie in the same line • Non Collinear – points that do not lie in the same line 7, Gd2A

13. Classifying Triangles • By Sides • Equilateral: equal sides • Isosceles: 2 sides the same • Scalene: no sides the same • By Angles • Equiangular: equal angles • Acute: all angles less than 90˚ • Obtuse: one angle greater than 90˚ • Right: one angle equal to 90˚

14. Parallel and Perpendicular Lines • Parallel Lines • have the same slope (m) • Perpendicular Lines • have opposite reciprocal slopes 7, Gd2B

15. Interpreting Parallel and Perpendicular Situations • Example: Which of the following best describes the graph of the equations below? y = 6 – 3x 3y = x + 6 y = -3x + 6 m = -3 3 3 3 • The lines have the same x-intercept • The lines have the same y-intercept • The lines intersect to form right angles • The lines are parallel to each other Perpendicular Lines! 7, Gd2B

16. Distance Formula • To find the distance between 2 points on a graph use the DISTANCE FORMULA • Example: What is the approximate length of when the coordinates of its endpoints are (-3, -9) and (5, 2)? • 13.6 • 7.3 • 9.1 • 11.7 7, Gd2C

17. Distance by Graphing • Example: What is the approximate length of when the coordinates of its endpoints are (-3, -9) and (5, 2)? 8 units • 13.6 • 7.3 • 9.1 • 11.7 11 units 7, Gd2C

18. Midpoint Formula • To find the midpoint between two points on the graph use the MIDPOINT FORMULA! • Example: Find the midpoint of the line segment whose endpoints are (5.75, 2) and (-3.25, 9). = = 7, Gd2C

19. A (-10, 6) B M (2, -1) D C Midpoint Formula… Backwards • Example: The midpoint of diagonals of rectangle ABCD is (2, - 1). The coordinates of A are (-10, 6). What are the coordinates of C? A. (-4, 2.5) B. (14, -8) C. (-8, 5) D. (-22, 13) -10 6 A +12 -7 M 2 -1 +12 -7 C 14 -8 7, Gd2C

20. Faces, Edges and Vertices • Faces are sides • Edges are lines • Verticesare corners 5 8 5 7 15 10 Faces: __, Edges: __, Vertices: __ 7, Ge2D

21. Other 3-D Shapes 0 0 0 • Sphere • Hemisphere • Cone • Cylinder Faces:__, Edges:__, Vertices:__ 1 0 0 Faces:__, Edges:__, Vertices:__ 1 0 1 Faces:__, Edges:__, Vertices:__ 2 0 0 Faces:__, Edges:__, Vertices:__ 7, Ge2D