Each symmetry in D 3 .

Question

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Answer 1

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 1, Problem 1E

To determine

To Describe:Each symmetry in D₃.

Expert Solution & Answer

Explanation of Solution

Given: An equilateral triangle.

Calculation:

Three rotations at 0, 120 and 240 gives the symmetric in an equilateral triangle and also flips over three different axes (vertex) at the midpoint of the opposite side gives the symmetric in an equilateral triangle. So total there are six symmetries in equilateral triangle.

The three rotations at 0, 120 and 240 which gives the symmetric are:

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 1

The three symmetries obtain by flips over three different axes are -

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 2

Thus, there are six symmetries in equilateral triangle.

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Students have asked these similar questions

e). n! (n - 1)!

Suppose you flip a fair two-sided coin four times and record the result. a). List the sample space of this experiment. That is, list all possible outcomes that could occur when flipping a fair two-sided coin four total times. Assume the two sides of the coin are Heads (H) and Tails (T).

e). n! (n - 1)!

Answer 2

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 1, Problem 1E

To determine

To Describe:Each symmetry in D₃.

Expert Solution & Answer

Explanation of Solution

Given: An equilateral triangle.

Calculation:

Three rotations at 0, 120 and 240 gives the symmetric in an equilateral triangle and also flips over three different axes (vertex) at the midpoint of the opposite side gives the symmetric in an equilateral triangle. So total there are six symmetries in equilateral triangle.

The three rotations at 0, 120 and 240 which gives the symmetric are:

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 1

The three symmetries obtain by flips over three different axes are -

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 2

Thus, there are six symmetries in equilateral triangle.

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Answer 3

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 1, Problem 1E

To determine

To Describe:Each symmetry in D₃.

Expert Solution & Answer

Explanation of Solution

Given: An equilateral triangle.

Calculation:

Three rotations at 0, 120 and 240 gives the symmetric in an equilateral triangle and also flips over three different axes (vertex) at the midpoint of the opposite side gives the symmetric in an equilateral triangle. So total there are six symmetries in equilateral triangle.

The three rotations at 0, 120 and 240 which gives the symmetric are:

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 1

The three symmetries obtain by flips over three different axes are -

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 2

Thus, there are six symmetries in equilateral triangle.

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Answer 4

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 1, Problem 1E

To determine

To Describe:Each symmetry in D₃.

Expert Solution & Answer

Explanation of Solution

Given: An equilateral triangle.

Calculation:

Three rotations at 0, 120 and 240 gives the symmetric in an equilateral triangle and also flips over three different axes (vertex) at the midpoint of the opposite side gives the symmetric in an equilateral triangle. So total there are six symmetries in equilateral triangle.

The three rotations at 0, 120 and 240 which gives the symmetric are:

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 1

The three symmetries obtain by flips over three different axes are -

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 2

Thus, there are six symmetries in equilateral triangle.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 1, Problem 1E

To determine

To Describe:Each symmetry in D₃.

Expert Solution & Answer

Explanation of Solution

Given: An equilateral triangle.

Calculation:

Three rotations at 0, 120 and 240 gives the symmetric in an equilateral triangle and also flips over three different axes (vertex) at the midpoint of the opposite side gives the symmetric in an equilateral triangle. So total there are six symmetries in equilateral triangle.

The three rotations at 0, 120 and 240 which gives the symmetric are:

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 1

The three symmetries obtain by flips over three different axes are -

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 2

Thus, there are six symmetries in equilateral triangle.

Answer 6

Chapter 1, Problem 1E

To determine

To Describe:Each symmetry in D₃.

Expert Solution & Answer

Explanation of Solution

Given: An equilateral triangle.

Calculation:

Three rotations at 0, 120 and 240 gives the symmetric in an equilateral triangle and also flips over three different axes (vertex) at the midpoint of the opposite side gives the symmetric in an equilateral triangle. So total there are six symmetries in equilateral triangle.

The three rotations at 0, 120 and 240 which gives the symmetric are:

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 1

The three symmetries obtain by flips over three different axes are -

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 2

Thus, there are six symmetries in equilateral triangle.

Answer 7

Chapter 1, Problem 1E

To determine

To Describe:Each symmetry in D₃.

Answer 8

Expert Solution & Answer

Explanation of Solution

Given: An equilateral triangle.

Calculation:

Three rotations at 0, 120 and 240 gives the symmetric in an equilateral triangle and also flips over three different axes (vertex) at the midpoint of the opposite side gives the symmetric in an equilateral triangle. So total there are six symmetries in equilateral triangle.

The three rotations at 0, 120 and 240 which gives the symmetric are:

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 1

The three symmetries obtain by flips over three different axes are -

Contemporary Abstract Algebra, Chapter 1, Problem 1E , additional homework tip 2

Thus, there are six symmetries in equilateral triangle.