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

© A Very Good Teacher 2007

Exit Level

TAKS Preparation UnitObjective 7


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


Cubes and Rectangular Prisms• The net of a cube is made entirely of

squares

• The net of a rectangular prism contains rectangles

7, Gb1B


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


Prisms with other bases• A Pentagonal Prism has a pentagon for

its bases

• A Hexagonal Prism has a hexagon for its bases

7, Gb1B


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.


Views of 3-D Solids• You must be able to imagine a 3-D solid

from every angle

7, Gd1C

Top

Front

Front

Right

Left

Right

Left

13 2

2

1

1


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?

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Front Right

A. B.

C. D.


Quadrilaterals (four sided figures)

• Rectangle

• Square

• Rhombus

• Trapezoid

• Parallelogram

7, Gd2A

Isosceles Trapezoid


Other Important Shapes

• Pentagon – five sided

• Hexagon – six sided

• Regular – perfect shape

– All sides congruent

– All angles congruent

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The Coordinate Plane

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Quadrant IQuadrant II

Quadrant III Quadrant 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)


Key Geometry Terms• Collinear – points that lie in the same line

• Non Collinear – points that do not lie in the same line

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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˚


Parallel and Perpendicular Lines

• Parallel Lines – have the same slope (m)

• Perpendicular Lines – have opposite

reciprocal slopes

7, Gd2B

1

2

Risem

Run

1

2

1

2

2

1


Interpreting Parallel and Perpendicular Situations

• Example: Which of the following best describes the graph of the equations below?

y = 6 – 3x

3y = x + 6

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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 + 6

3 3 3

12

3y x

m = -31

3m

Perpendicular Lines!


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)?

2 22 1 2 1( ) ( )d x x y y

XY2y2x1y1x

2 25 3 2 9d

2 28 11d

64 121d 185d

A. 13.6 B. 7.3C. 9.1D. 11.7

7, Gd2C


Distance by Graphing• Example: What is the approximate length of

when the coordinates of its endpoints are (-3, -9) and (5, 2)?

XY

A. 13.6 B. 7.3C. 9.1D. 11.7

11 units

8 units

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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).

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1 2 1 2,2 2

x x y y

1.25,5.5

2.5 11,

2 2

5.75 3.25 2 9,

2 2

=

=


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

C D X Y

AMC

-10 62 -114 -8

+12

+12

-7

-7

7, Gd2C


Faces, Edges and Vertices• Faces are sides

• Edges are lines

• Vertices are corners

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Faces: __, Edges: __, Vertices: __5 8 57 15 10


Other 3-D Shapes

• Sphere

• Hemisphere

• Cone

• Cylinder

Faces:__, Edges:__, Vertices:__




0 0 0

1 0 0

1 0 1

2 0 0

7, Ge2D

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

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