Exit Level TAKS Preparation Unit Objective 7 A

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, Gb 1 B © 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, Gb 1 B © 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, Gb 1 B © 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, Gb 1 B © 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, Gb 1 B © 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, Gd 1 C 3 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, Gd 1 C © A Very Good Teacher 2007

Quadrilaterals (four sided figures) • Rectangle • Square • Rhombus Isosceles Trapezoid • Trapezoid • Parallelogram 7, Gd 2 A © A Very Good Teacher 2007

Other Important Shapes • Pentagon – five sided • Hexagon – six sided • Regular – perfect shape – All sides congruent – All angles congruent 7, Gd 2 A © 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, Gd 2 A © 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, Gd 2 A © 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, Gd 2 B © A Very Good Teacher 2007

Interpreting Parallel and Perpendicular Situations • Example: Which of the following best describes the graph of the equations below? y = -3 x + 6 m = -3 y = 6 – 3 x 3 y = x + 6 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, Gd 2 B © 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. 13. 6 B. 7. 3 C. 9. 1 D. 11. 7 7, Gd 2 C © 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. C. D. 8 units 13. 6 7. 3 9. 1 11. 7 11 units 7, Gd 2 C © 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, Gd 2 C © 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 A. (-4, 2. 5) B. (14, -8) C. (-8, 5) D. (-22, 13) (-10, 6) M (2, -1) D X -10 +12 A C Y 6 M 2 -1 +12 C 14 -8 7, Gd 2 C -7 -7 © A Very Good Teacher 2007

Faces, Edges and Vertices • Faces are sides • Edges are lines • Vertices are corners 5 8 Vertices: 10 5 Faces: __, __ 7 Edges: 15 7, Ge 2 D © A Very Good Teacher 2007

Other 3 -D Shapes 0 0 0 1 0 1 2 0 0 • Sphere Faces: __, Edges: __, Vertices: __ • Hemisphere Faces: __, Edges: __, Vertices: __ • Cone Faces: __, Edges: __, Vertices: __ • Cylinder Faces: __, Edges: __, Vertices: __ 7, Ge 2 D © A Very Good Teacher 2007