Consider a rhombus that is not square (i.e., the four sides all have the same length, but the angles between sides is not 90°).

Consider a rhombus that is not square (i.e., the four sides all have the same length, but the angles between sides is not 90°). Describe all the symmetries of the rhombus. Write down the Cayley table for the group of symmetries,

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

In Euclidean geometry, a rhombus is a simple quadrilateral whose four sides all have the same...

In Euclidean geometry, a rhombus is a simple quadrilateral whose four sides all have the same length. If lengths of each of the sides are a and the distance between the parallel sides (known as height) is h, then the area of the rhombus is defined as a × h. Suppose that you already have a class named Rhombus that can hold a and h. The class has a method to compute the area as well. The class is as...

All of the sides of a quadrilateral are congruent if it is a rhombus.

The following conditional statement is true.All of the sides of a quadrilateral are congruent if it is a rhombus.Which of the following statements must also be true?a) If not all of the sides of a quadrilateral are congruent, then it is not a rhombus.b) If a quadrilateral is not a rhombus, then all of its sides are not congruent.c) If a quadrilateral is a rhombus, then not all of its sides are congruent.d) If all of the sides of a...

A square membrane has all four sides (length a) tightly clamped. Some of its vibrational modes...

A square membrane has all four sides (length a) tightly clamped. Some of its vibrational modes are also dampened by a clamp placed at the center of the membrane. Find the first four distinct vibrational frequencies of this "square drum."

PYTHON: A rhombus is a parallelogram with four equal sides. It resembles the diamonds suit in...

PYTHON: A rhombus is a parallelogram with four equal sides. It resembles the diamonds suit in playing cards. Here are the properties of a rhombus: - opposite sides are parallel - all four sides have the same length - opposite angles are equal - sum of any 2 adjacent angles is 180 degrees (x + y = 180 degrees) Write a function called rhombus that uses turtle graphics to draw a rhombus. The function rhombus takes three parameters: 1. t,...

Electrostatic Force and Equilibrium Consider a rhombus with side of length L. The rhombus has two...

Electrostatic Force and Equilibrium Consider a rhombus with side of length L. The rhombus has two pair of equal interior angles. Label one of these pair θ and the other φ. Four identical, positive point charges, q are placed on the vertices of the rhombus. Draw the configuration. a) Obtain a symbolic expression for the electric field at one of the vertices (your choice) and then at an adjacent vertex (Do you now know the electric field at all of...

Four charges of magnitude +q are placed at the corners of a square whose sides have...

Four charges of magnitude +q are placed at the corners of a square whose sides have a length d. What is the magnitude of the total force exerted by the four charges on a charge Q located a distance b along a line perpendicular to the plane of the square and equidistant from the four charges? Ans: bqQ/πε 0 (b2 + d2 / 2) how to get this answer?

Let S be the square centered at the origin with sides of length 2, and C...

Let S be the square centered at the origin with sides of length 2, and C be the unit circle centered at the origin. (a) If you randomly throw a point on S, what is the probability that it will lie in C? Ans: 0.785 (b) Describe how you could use simulation to estimate the probability in part (a). (c) How can you use simulation to estimate a? For part b and c, there maybe a need to generate random...

The baseball diamond at Grayson Stadium is a square with 90 ft sides. A batter hits...

The baseball diamond at Grayson Stadium is a square with 90 ft sides. A batter hits the ball and runs to the right toward first base with a constant speed of 24 ft/s. At the same time a runner on 3rd base runs home at a constant speed of 28 ft/s. At what rate is the distance between the two runners changing two seconds after they start running?

A pentagon is formed by adding two sides of the same length to attach an isoceles...

A pentagon is formed by adding two sides of the same length to attach an isoceles triangle to one side of a rectangle. If the area is fixed at A, what are the dimensions (in terms of A) that will minimize the pentagon's perimeter?

Consider four nonstandard dice, whose sides are labeled as follows (the 6 sides on each die...

Consider four nonstandard dice, whose sides are labeled as follows (the 6 sides on each die are equally likely). A: 4, 4, 4, 4, 0, 0 B: 3, 3, 3, 3, 3, 3 C: 6, 6, 2, 2, 2, 2 D: 5, 5, 5, 1, 1, 1 These four dice are each rolled once. Let A be the result for die A, B be the result for die B, etc. (a) Find P(A > B), P(B > C), P(C >D),...

Subjects