© A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 7

© A Very Good Teacher 2007 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

© A Very Good Teacher 2007 Cubes and Rectangular Prisms The net of a cube is made entirely of squares The net of a rectangular prism contains rectangles 7, Gb1B

© A Very Good Teacher 2007 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

© A Very Good Teacher 2007 Prisms with other bases A Pentagonal Prism has a pentagon for its bases A Hexagonal Prism has a hexagon for its bases 7, Gb1B

© A Very Good Teacher 2007 Use your imagination! Example: The net below can be folded to form a cube. Which cube could be formed from this net? 7, Gb1B A. B. C. D.

© A Very Good Teacher 2007 Views of 3-D Solids You must be able to imagine a 3-D solid from every angle 7, Gd1C Top Front Right Left Right Left

© A Very Good Teacher 2007 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? 7, Gd1C Front Right A. B. C. D.

© A Very Good Teacher 2007 Quadrilaterals (four sided figures) Rectangle Square Rhombus Trapezoid Parallelogram 7, Gd2A Isosceles Trapezoid

© A Very Good Teacher 2007 Other Important Shapes Pentagon – five sided Hexagon – six sided Regular – perfect shape –All sides congruent –All angles congruent 7, Gd2A

© A Very Good Teacher 2007 The Coordinate Plane 7, Gd2A Quadrant IQuadrant II Quadrant IIIQuadrant IV x-axis y-axis An ordered pair (point) is graphed by using the x to move right or left and the y to move up or down (x, y) (2, 5) (-3, -5)

© A Very Good Teacher 2007 Key Geometry Terms Collinear – points that lie in the same line Non Collinear – points that do not lie in the same line 7, Gd2A

© A Very Good Teacher 2007 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˚

© A Very Good Teacher 2007 Parallel and Perpendicular Lines Parallel Lines –have the same slope (m) Perpendicular Lines –have opposite reciprocal slopes 7, Gd2B

© A Very Good Teacher 2007 Interpreting Parallel and Perpendicular Situations Example: Which of the following best describes the graph of the equations below? y = 6 – 3x 3y = x + 6 7, Gd2B A.The lines have the same x-intercept B.The lines have the same y-intercept C.The lines intersect to form right angles D.The lines are parallel to each other y = -3x m = -3 Perpendicular Lines!

© A Very Good Teacher 2007 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)? A B. 7.3 C. 9.1 D , Gd2C

© A Very Good Teacher 2007 Distance by Graphing Example: What is the approximate length of when the coordinates of its endpoints are (-3, -9) and (5, 2)? A B. 7.3 C. 9.1 D units 8 units 7, Gd2C

© A Very Good Teacher 2007 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 = =

© A Very Good Teacher 2007 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) A (-10, 6) M (2, -1) B CD XY A M C , Gd2C

© A Very Good Teacher 2007 Faces, Edges and Vertices Faces are sides Edges are lines Vertices are corners 7, Ge2D Faces: __, Edges: __, Vertices: __

© A Very Good Teacher 2007 Other 3-D Shapes Sphere Hemisphere Cone Cylinder Faces:__, Edges:__, Vertices:__ , Ge2D