Based on triangulation of polygons, prove that copies of a regular n- gon can tile the plane only for n= 3,4 , and 6.

Q: Exercise 1. Find the area of the polygon in R³ with corners (3, –4) (-7, 7), (5, 5), (–5, –6) and

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Q: cube of edge 4 is in cut by a plane containing two teo diagonally opposite edges of the cube. Find…

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Q: Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 3,…

A: Consider the provided question, Let the vertices of the parallelepiped are A, B, C and D.

Q: Find the area of a triangle formed by the points (8, – 5), – 7) and (5, 1) by using Herones formula…

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Q: Which of the following would show that the diagonals of quadrilateral JKLM on the coordinate plane…

A: The given triangle JKLM is,

Q: The quadrilateral ABCD is inseribed in the eircle centered at the point o. B(2y)°

A: Given that the quadrilateral ABCD is inscribed in the circle centred at the point O.

Q: Show that the quadrilateral with the given vertices is a trapezoid. Then decide whether it is…

A: Find if the figure is an isosceles trapezoid and find all the 4 slopes.

Q: 2. If there are seven distinct points on a plane with no three are collinear, how many different…

A: A polygon requires at least 3 points (and 3 sides). Since no 3 points are collinear, that means you…

Q: 6. Show that the diagonals of the square with the given vertices are congruent perpendicular…

A: The formula for the midpoints of (x1,y1) and (x2,y2) is x2+x12,  y2+y12 and the formula for the…

Q: How many triangles can be formed from 11 distinct points on the plane, no three points of which are…

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Q: In an artistic design by a contractor of the students’ centre in a university, four pillars were…

A: Given: In an artistic design, four pillars were erected to form two triangular figures with the…

Q: Prove that C is on the perpendicular bisector of segment AB.

A: Consider the given vertices A-3,2, B5,-4, and C7,7. If C is on the perpendicular bisector of AB,…

Q: 2) Find the area of triangular ABC of points (4,6,12), (2,7,6) and (-2,5,6).

A: From the given data:

Q: Prove a quadrilateral with vertices G(1,1), H(5,3), I(4,5) and J(0,3) is a rectangle

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Q: Prove that the diagonals of a rectangle are of equal length. [Hint: Take the vertices of the…

A: To prove that diagonals of a rectangle are if equal length.  Consider a rectangle which has one…

Q: Let Q be the quadrilateral with vertices (−2, 3), (1, 4), (3, 0), and (−1, −3). Find the area of Q.

A: Given that, Q be the quadrilateral whose vertices are −2, 3), (1, 4), (3, 0), and (−1, −3). To find:…

Q: アon) usweris X10 बप्कणs In the ry-plane, what is the perimeter of an equilateral triangle with one…

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Q: does a 12-sided co

A: Here we have to find the number of diagonals of a 12-sided convex polygon.

Q: what are the possible dimensions of their largest rug?

A: The length of the smaller rug = l = 3 feetThe breadth of of the smaller rectangle = b = 2 feetLet…

Q: 4 - Find the volume of a parallelepiped if four of its eight vertices are A(0, 0, 0), B(1, 2, 0),…

A: The given vertices are: A = (0, 0, 0) B = (1, 2, 0) C = (0, -3, 2) D = (3, -4, 5)

Q: . Prove that in a triangle, the orthocenter, centroid and the circumcenter are concurrent (in a…

A: Let X be the mid-point of EF Construct the median DX. Since G is the centroid, G is on DX by the…

Q: 2. Show that the points A(2,2,2), B(2,0,1), C(4, 1, – 1) and D(4, 3,0) are coplanar and that they…

A: The solution are next step

Q: A cube has four diagonals. Show that no two of them are perpendicular.

A: Given: A cube has four diagonals.

Q: Prove that C is on the perpendicular bisector of segment AB.

A: Solution:Given A(-4,-3), B(6,1) and C (5,-11)To Prove: C is perpendicular bisector of ABi.e., to…

Q: Prove that the points 3,0),(4, 5),(-1, 4) and (-2,-1) taken in order, Lorm a rhombus, also find its…

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Q: Find the volume of the parallelepiped with one vertex at (4, 3, 1), and adjacent vertices at (6,…

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Q: Find the volume of a parallelepiped if four of its eight vertices are A(0, 0, 0), B(1, 2, 0), C(0,…

A: Draw the diagram roughly

Q: Enter a whole number. To tessellate a plane with squares, hexagons, and dodecagons, one needs…

A: Tessellate a plane with the given figure means joining the given figure number of times to get the…

Q: A quadrilateral has vertices A = (0, 0), B = (2,4), C = (0,5), and D = (-2, 1). Prove ABCD is a…

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Q: IFA and B have 6 and 9 elements each, what is the minimum number of elements Aunion B?*

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Q: Prove that a parallelogram is a rectangle if and only if its diagonals are equal in length. (This…

A: Let ABCD be a parallelogram. Given AC and BD are diagonals of parallelogram in equal length. In…

Q: 2 Prove that a quadrilateral with the vertices A(-2,3), B(2,6), C(7,6) and D(3,3) is a rhombus. IB

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Q: Prove that a parallelo-gram is a rectangle if and only if its diagonals are equal in length. (This…

A: Consider a parallelogram ABCD having diagonals AC and BD such that, AC=BD.

Q: 5. Find the dimension of the largest rectangular building that can be placed on a right-triangular…

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Q: what is the maximum interior angle possible for a regular p olygon?

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Q: Every polyhedron can be unfolded into a two-dimensional flat surface. O True O False

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Q: When parallelograms are rectangles Prove that a parallelogram is a rectangle if and only if its…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Calculate the volume of a parallelepiped if four of its eight vertices are A (1, 2, 4) , B (2, 0,…

A: Given that: A(1,2,4), B(2,0,5), C(7,1,-2) and (4,3,1)

Q: 27. How many triangles collinear points? can 'be drawn on a plane using 8 non-

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Q: If there are 7 distinct points on a plane with no three of which are collinear, how many different…

A: A polygon is a closed shape in two dimensional. It do not contain any curves. Thus the minimum…

Q: Prove analytically that in any triangle the perpendiculars drawn from the vertices upon the opposite…

A: Given-  the perpendiculars drawn from the vertices upon the opposite sides. To prove-the altitudes…

Q: For any cyclic quadrilateral, the product of the diagonals equals the sum of the products of the…

A: Here we have to determine the name of the theorem. The given theorem is: For any cyclic…

Q: Let Q be the quadrilateral with vertices (-2,3), (1,4), (3,0), and (-1,–3). Find the area of Q

A: Consider a quadrilateral Q with vertices  A−2,3,B1,4,C3,0 and D−1,−3

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

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Q: Show that the quadrilateral having vertices at (1, 1,3), (-2,1,-1), (-5,4, 0), and (-8, 4,-4) is a…

A: This is a problem related to area of the parallelogram by cross products. Based on the general…

Q: A quadrilateral has vertices A = (0, 0), B= (2,4), C = (0,5), and D = (-2, 1). Prove ABCD is a…

A: Given :

Q: 2) DRAW RIGHT-HAND INVOLUTE OF SQUARE. USE D AS FIRST CENTER. A

A: Involute of square of dimension 1 unit D as a first centre (drawn in picture)

Q: Prove that if two pairs of opposite edges of a tetrahedron are perpendicular, then the third pair is…

A: Consider the tetrahedron  ABCD and let two pairs of opposite sides are perpendicular. Consider the…