Physics High-speed photography makes itpossible to analyze the physics behind awater

Vocabulary Apply the vocabulary from this lesson to answer each question Describe the line of symmetry of an isosceles triangle.

Vocabulary Apply the vocabulary from this lesson to answer each question The capital letter T has ? . (line symmetry or rotational symmetry)

Tell whether each figure has line symmetry. If so, copy the shape and draw all lines of symmetry 3

Tell whether each figure has line symmetry. If so, copy the shape and draw all lines of symmetry 4

Tell whether each figure has line symmetry. If so, copy the shape and draw all lines of symmetry 5

Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry 6

Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry 7

Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry 8

Architecture The Pentagon in Alexandria, Virginia, is the worlds largest office building. Copy the shape of the building and draw all lines of symmetry. Give the angle and order of rotational symmetry

Tell whether each figure has plane symmetry, symmetry about an axis, or neither. prism

Tell whether each figure has plane symmetry, symmetry about an axis, or neither. cylinder

Tell whether each figure has plane symmetry, symmetry about an axis, or neither. rectangular prism

Tell whether each figure has line symmetry. If so, copy the shape and draw all lines of symmetry 13

Tell whether each figure has line symmetry. If so, copy the shape and draw all lines of symmetry 14

Tell whether each figure has line symmetry. If so, copy the shape and draw all lines of symmetry 15

Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry. 16

Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry. 17

Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry. 18

Art Op art is a style of art that uses optical effects to create an impression of movement in a painting or sculpture. The painting at right, Vega-Tek, by Victor Vasarely, is an example of op art. Sketch the shape in the painting and draw any lines of symmetry. If there is rotational symmetry, give the angle and order.

Tell whether each figure has plane symmetry, symmetry about an axis, or neither. sphere

Tell whether each figure has plane symmetry, symmetry about an axis, or neither. triangular pyramid

Tell whether each figure has plane symmetry, symmetry about an axis, or neither. torus

Draw a triangle with the following number of lines of symmetry. Then classify the triangle. exactly one line of symmetry

Draw a triangle with the following number of lines of symmetry. Then classify the triangle. three lines of symmetry

Draw a triangle with the following number of lines of symmetry. Then classify the triangle. no lines of symmetry

Data Analysis The graph shown, called the standard normal curve, is used in statistical analysis. The area under the curve is 1 square unit. There is a vertical line of symmetry at x = 0. The areas of the shaded regions are indicated on the graph. Find the area under the curve for x > 0.

Data Analysis The graph shown, called the standard normal curve, is used in statistical analysis. The area under the curve is 1 square unit. There is a vertical line of symmetry at x = 0. The areas of the shaded regions are indicated on the graph. Find the area under the curve for x > 3.

Data Analysis The graph shown, called the standard normal curve, is used in statistical analysis. The area under the curve is 1 square unit. There is a vertical line of symmetry at x = 0. The areas of the shaded regions are indicated on the graph. If a point under the curve is selected at random, what is the probability that the x-value of the point will be between -1 and 1?

Tell whether the figure with the given vertices has line symmetry and/or rotational symmetry. Give the angle and order if there is rotational symmetry. Draw the figure and any lines of symmetry. A (-2, 2) , B (2, 2) , C (1, -2) , D (-1, -2)

Tell whether the figure with the given vertices has line symmetry and/or rotational symmetry. Give the angle and order if there is rotational symmetry. Draw the figure and any lines of symmetry. R (-3, 3) , S (3, 3) , T (3, -3) , U (-3, -3)

Tell whether the figure with the given vertices has line symmetry and/or rotational symmetry. Give the angle and order if there is rotational symmetry. Draw the figure and any lines of symmetry. J (4, 4) , K (-2, 2) , L (2, -2)

Tell whether the figure with the given vertices has line symmetry and/or rotational symmetry. Give the angle and order if there is rotational symmetry. Draw the figure and any lines of symmetry. A (3, 1) , B (0, 2) , C (-3, 1) , D (-3, -1) , E (0, -2) , F (3, -1)

Art The Chokwe people of Angola are known for their traditional sand designs. These complex drawings are traced out to illustrate stories that are told at evening gatherings. Classify the symmetry of the Chokwe design shown.

Algebra Graph each function. Tell whether the graph has line symmetry and/or rotational symmetry. If there is rotational symmetry, give the angle and order. Write the equations of any lines of symmetry y = x 2

Algebra Graph each function. Tell whether the graph has line symmetry and/or rotational symmetry. If there is rotational symmetry, give the angle and order. Write the equations of any lines of symmetry y = (x - 2)2

Algebra Graph each function. Tell whether the graph has line symmetry and/or rotational symmetry. If there is rotational symmetry, give the angle and order. Write the equations of any lines of symmetry y = x 3

This problem will prepare you for the Concept Connection on page 880. This woodcut, entitled Circle Limit III, was made by Dutch artist M. C. Escher. a. Does the woodcut have line symmetry? If so, describe the lines of symmetry. If not, explain why not. b. Does the woodcut have rotational symmetry? If so, give the angle and order of the symmetry. If not, explain why not. c. Does your answer to part b change if color is not taken into account? Explain.

Classify the quadrilateral that meets the given conditions. First make a conjecture and then verify your conjecture by drawing a figure. two lines of symmetry perpendicular to the sides and order-2 rotational symmetry

Classify the quadrilateral that meets the given conditions. First make a conjecture and then verify your conjecture by drawing a figure. no line symmetry and order-2 rotational symmetry

Classify the quadrilateral that meets the given conditions. First make a conjecture and then verify your conjecture by drawing a figure. two lines of symmetry through opposite vertices and order-2 rotational symmetry

Classify the quadrilateral that meets the given conditions. First make a conjecture and then verify your conjecture by drawing a figure. four lines of symmetry and order-4 rotational symmetry

Classify the quadrilateral that meets the given conditions. First make a conjecture and then verify your conjecture by drawing a figure. one line of symmetry through a pair of opposite vertices and no rotational symmetry

Physics High-speed photography makes it possible to analyze the physics behind a water splash. When a drop lands in a bowl of liquid, the splash forms a crown of evenly spaced points. What is the angle of rotational symmetry for a crown with 24 points?

Critical Thinking What can you conclude about a rectangle that has four lines of symmetry? Explain.

Geography The Isle of Man is an island in the Irish Sea. The islands symbol is a triskelion that consists of three running legs radiating from the center. Describe the symmetry of the triskelion.

Critical Thinking Draw several examples of figures that have two perpendicular lines of symmetry. What other type of symmetry do these figures have? Make a conjecture based on your observation.

Each figure shows part of a shape with a center of rotation and a given rotational symmetry. Copy and complete each figure. order 4

Each figure shows part of a shape with a center of rotation and a given rotational symmetry. Copy and complete each figure. order 6

Each figure shows part of a shape with a center of rotation and a given rotational symmetry. Copy and complete each figure. order 2

Write About It Explain the connection between the angle of rotational symmetry and the order of the rotational symmetry. That is, if you know one of these, explain how you can find the other.

What is the order of rotational symmetry for the hexagon shown? 2 3 4 6

Which of these figures has exactly four lines of symmetry? Regular octagon Isosceles triangle Equilateral triangle Square

Consider the graphs of the following equations. Which graph has the y-axis as a line of symmetry? y = (x - 3)2 y = x 3 y = x 2 - 3 y = x + 3

Donnell designed a garden plot that has rotational symmetry, but not line symmetry. Which of these could be the shape of the plot?

A regular polygon has an angle of rotational symmetry of 5. How many sides does the polygon have?

How many lines of symmetry does a regular n-gon have if n is even? if n is odd? Explain your reasoning.

Find the equation of the line of symmetry for the graph of each function y = (x + 4)2

Find the equation of the line of symmetry for the graph of each function y = x - 2

Find the equation of the line of symmetry for the graph of each function y = 3x 2 + 5

Give the number of axes of symmetry for each regular polyhedron. Describe all axes of symmetry cube

Give the number of axes of symmetry for each regular polyhedron. Describe all axes of symmetry tetrahedron

Give the number of axes of symmetry for each regular polyhedron. Describe all axes of symmetry octahedron

Shari worked 16 hours last week and earned $197.12. The amount she earns in one week is directly proportional to the number of hours she works in that week. If Shari works 20 hours one week, how much does she earn? (Previous course)

Find the slant height of each figure. (Lesson 10-5) a right cone with radius 5 in. and surface area 61 in 2

Find the slant height of each figure. (Lesson 10-5) a square pyramid with lateral area 45 cm 2 and surface area 65.25 cm 2

Find the slant height of each figure. (Lesson 10-5) a regular triangular pyramid with base perimeter 24 3 m and surface area 120 3 m 2

Determine the coordinates of the final image of the point P (-1, 4) under each composition of isometries. (Lesson 12-4) Reflect point P across the line y = x and then translate it along the vector 2, -4.

Determine the coordinates of the final image of the point P (-1, 4) under each composition of isometries. (Lesson 12-4) Rotate point P by 90 about the origin and then reflec

Determine the coordinates of the final image of the point P (-1, 4) under each composition of isometries. (Lesson 12-4) Translate point P along the vector 1, 0 and then rotate it 180 about the origin