) List the four rigid motions on the plane b) What are the three regular tessellations (tilings)of a plane c) What are the five Platonic solids

Q: Which of the shapes below can make a regular tessellation of the plane? O Regular hexagon O Regular…

A: Regular tessellation - it is a regular pattern made of flat shapes by repeatition of that shape and…

Q: Assume that the Earth is a sphere. Howmany points are there on the Earth's surfacethat are…

A: In case of sphere, two points are equidistant from many points. Therefore their are infinite points…

Q: Show that the triangle with vertices A(7,8), B(1, 20), C(1, 10) is an isosceles right ti plane model…

A: Given: To explain the given statement as follows, In the upper half-plane model for hyperbolic…

Q: Is the set c~(R* U {0}) “the entire plane without the non-negative reals" conformally equivalent to…

A: We need to evaluate the statement "the entire plane without non negative reals, ℂ-{ℝ∪{0}}, is…

Q: 5a. Consider the right square pyramid with a horizontal plane intersecting the pyramid halfway up…

A: The horizontal plane will be parallel to the base of the pyramid.

Q: (b) Let the distance between two adjacent planes parallel to the plane (hkf) in the direct lattice…

A:

Q: Let ABCD be an isosceles trapezoid having parallel bases AB and CD with AB > CD.Line segments from a…

A: Consider the following figure.

Q: In the strip of rectangles shown below, a certain rigid motion applied to the leftmost rectangle…

A: The given pattern has vertical reflection symmetry since it would have two mirror images if we draw…

Q: 3. Prove that a flat surface of revolution is part of a plane, cone, or cylinder.

A: prove that a flat surface of revolution is part of plane or cone or cylinder. solution a flat…

Q: Draw an obtuse triangle and, by construction, find the centroid of the triangle. (HINT: Begin by…

A: To get an obtuse triangle, draw a triangle with one of its interior angle should be greater than…

Q: The volume of the pyramid formed in the first octant by the plane 6x + 10y + 5z-30 = 0 is: О 45 О зо…

A: We can solve as follows

Q: A cube with a cylinder cut from its center is cut along the plane shown. Which of the following is…

A: In this figure cube is just coated outside the cylinder

Q: Which of the shapes below can make a regular tessellation of the plane? O Square O Regular heptagon…

A:

Q: Every triangle has a balancing point, called the centroid. O True O False

A:

Q: iven

A: Given △ABC Let X be any point in the plane so that AX, BX, CX are cevians of △ABC given to prove…

Q: Determine the Miller indices of a plane that makes intercepts of (4, 3 and 8) on the coordinate axes…

A: To calculate Miller indices we have to take reciprocal of ratio of intercepts and axial length

Q: Prove that the midsegment of a trapezoid is parallel to the bases and its length is the average of…

A: To prove that the mid-segment of a trapezoid is parallel to its base, first consider a trapezoid…

Q: A space has the line element, ds? = v*du? +u*dv² . Determine whether this space is flat or curved.

A: It is given that the line element ds2=v2du2+u2dv2. it is required to determine that whether this…

Q: Show that if there is an Archimedean solid that has faces that are regular pentagons and equilateral…

A: Truncated tetrahedron: In geometry, An Archimedean solid is one of the 13 solids first enumerated by…

Q: 16. In a rhombus ABCD, AC = 24 cm and BD 10 cm. Calculate the perimeter of the rhombus. %3D %3D

A:

Q: Which of the shapes below can make a regular tessellation of the plane? O Regular octagon O Regular…

A:

Q: AABE = 11 in2, ABCE = 15 in2, ACDE = 11 in2, and ADAE = 9 in2. A solid slanted to the left has…

A:

Q: A cube with a cylinder cut from Its center is cut along the plane shown below. Which of the…

A: When the cube with a cylinder cut from its center is cut along the plane as shown in the figure,

Q: Find an inner product on R such that the unit sphere is the ellipsoid z? = 1, a, b, c > 0. c? y? a…

A: Let a,b,c>0 be three real numbers. Define a map ,:ℝ3×ℝ3→ℝ as follows:…

Q: Let A = set of all quadrilaterals B = set of all rectangles C = set of all equiangular polygons D =…

A:

Q: Draw the solid of revolution obtained by rotating the given plane region about line L. Which figure…

A:

Q: 1. Sketch an example of a convex heptagon and an example of a concave heptagon.

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Must the centroid of an isosceles triangle lie on the altitude to the base?

A: The centroid of an isosceles triangle lie on the altitude.

Q: Is plane ABC perpendicular with plane BCD? Prove by completing all views. Construct parallelogram…

A:

Q: Find the standard equatron of the sphere with the given chara ct eristics center:(-1,7 9) radius: 6

A:

Q: In space coordinates, the xy plane consists of all the points of the form O (0, y, z) O (X, y, z) O…

A:

Q: The barycentric coordinates of a point P with respect to the non-collinear points A, B,C is given by…

A:

Q: Consider again the one-link planar robot shown in Fig. P3.14. Determine the length / and angle 0 if…

A: Solution :-

Q: From the stereographic projection of the Lobachevsky plane from the north pole (0, 0, -R) on disk D…

A:

Q: Prove that the diagonals of a rhombus intersect at right angles. (A rhombus is a quadrilateral with…

A: We have to prove that diagonal of rhombus intersects at right angle. Let ABCD is a rhombus.…

Q: rclockwise, that encloses disk R in the plane. neck Answer. 71

A: Given : F = <5x^6y, 8xy^2 + 4x^7>

Q: Which of the following three-dimensional solids can be generated by rotating a two-dimensional…

A: Need to find which solid can be made by rotating a two dimensional figure about an axis.

Q: If there are 9 distinct points on a plane, no 3 of which are collinear, how many quadrilaterals can…

A:

Q: Write a complete proof to prove that the base angles of an Isosceles trapezold are congruent. Gven:…

A:

Q: A research facility is located at the centroid of the triangle made by highways connecting three…

A: Given: Distance between town P and Q is 6 mi. Distance of median from R meeting PQ at S say,…

Q: Assume the pattern of congruent squares shown in the figure continues forever. Write rules for rigid…

A:

Q: Does a right circular cone such as a wizard's cap have a) symmetry with respect to at least one…

A:

Q: Assume the pattern of congruent squares shown in the figure continues forever. Write rules for rigid…

A: Translation of a P(x,y): from (x,y) to P'(x+a,y+b)is shown as (x,y)→(x+a,y+b).

Q: 7. What additional piece is needed to prove JMLK is a rhombus ?

A:

Q: Which figure below cannot be tessellated? O Rhombus O Trapezoid O Heptagon O Square

A: Tessellation is a special pattern of shapes that fits together with no overlap or gaps.

Q: Exercises 9.4 1. Which of these two polyhedrons is concave? Note that the interior dihedral angle…

A: Definition: A concave polyhedron is a polyhedron with the property that there exist two points…

Q: of the Solids ebtaind by-revolding 5 Find the velume of the Sotids abtaind by revolu.ing Yegion in…

A: In this question we have to calculate the volume obtained by the revolution of given two region…

Q: Which rigid motion or sequence of rigid motions maps parallelogram ABCD onto parallelogram JKLM? A B…

A:

Q: Refer to the flgure below to name the following: 4. Name 3 collinear points: 5. Name 3 non-collinear…

A: Since you have posted multipart question I do first six subpart as perour company guidelines please…

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.