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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? A. B. C. D. 7, Gb1B © A Very Good Teacher 2007 Views of 3-D Solids • You must be able to imagine a 3-D solid from every angle Left Front Right Top Left Front Right 7, Gd1C 3 2 1 2 1 1 © 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? Front A. B. C. D. Right 7, Gd1C © A Very Good Teacher 2007 Quadrilaterals (four sided figures) • Rectangle • Square • Rhombus Isosceles Trapezoid • Trapezoid • Parallelogram 7, Gd2A © 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 y-axis An ordered pair (point) is graphed by Quadrant II using the x to move right or left and the y to move up or down Quadrant III (x, y) (2, 5) Quadrant I (-3, -5) x-axis Quadrant IV 7, Gd2A © 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 6 5 4 3 2 1 • Parallel Lines – have the same slope (m) Rise m Run -6 -5 -4 -3 -2 -1 • Perpendicular Lines 1 2 -6 -5 -4 -3 -2 -1 2 1 7, Gd2B 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 6 5 4 3 2 1 – have opposite reciprocal slopes y -1 -2 -3 -4 -5 -6 1 2 1 2 x 1 2 y x 1 2 3 4 5 6 2 1 © A Very Good Teacher 2007 Interpreting Parallel and Perpendicular Situations • Example: Which of the following best describes the graph of the equations below? y = -3x + 6 m = -3 y = 6 – 3x 1 1 3y = x + 6 m y x2 3 3 3 3 3 A. The lines have the same x-intercept B. The lines have the same y-intercept Perpendicular Lines! C. The lines intersect to form right angles D. The lines are parallel to each other 7, Gd2B © A Very Good Teacher 2007 Distance Formula • To find the distance between 2 points on a graph use the DISTANCE FORMULA d ( x2 x1 ) ( y2 y1 ) 2 2 • Example: What is the approximate length of XY when the xcoordinates ofy its y x 1 2 2 1 endpoints are (-3, -9) and (5, 2)? A. 13.6 B. 7.3 C. 9.1 D. 11.7 d 5 3 2 9 d 8 11 2 2 d 64 121 7, Gd2C 2 2 d 185 © A Very Good Teacher 2007 Distance by Graphing • Example: What is the approximate length of XY when the coordinates of its endpoints are (-3, -9) and (5, 2)? A. B. C. D. 8 units 13.6 7.3 9.1 11.7 11 units 7, Gd2C © A Very Good Teacher 2007 Midpoint Formula • To find the midpoint between two points on the graph use the MIDPOINT FORMULA! x1 x2 y1 y2 , 2 2 • Example: Find the midpoint of the line segment whose endpoints are (5.75, 2) and (-3.25, 9). 5.75 3.25 2 9 2.5 11 , = 2 ,2 2 2 = 1.25,5.5 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 B (-10, 6) A. (-4, 2.5) B. (14, -8) C. (-8, 5) D. (-22, 13) M (2, -1) D X -10 +12 A C Y 6 M 2 -1 +12 C 14 -8 7, Gd2C -7 -7 © A Very Good Teacher 2007 Faces, Edges and Vertices • Faces are sides • Edges are lines • Vertices are corners 5 8 Vertices: __ 5 Faces: __, __, 7 Edges: 15 10 7, Ge2D © A Very Good Teacher 2007 Other 3-D Shapes • Sphere 0 Edges:__, 0 Vertices:__ 0 Faces:__, • Hemisphere Faces:__, 1 Edges:__, 0 Vertices:__ 0 • Cone 1 Edges:__, 0 Vertices:__ 1 Faces:__, • Cylinder Faces:__, 2 Edges:__, 0 Vertices:__ 0 7, Ge2D © A Very Good Teacher 2007