If squares are erected externally on the sides of a parallelogram then their centers are the vertices of a square. Justify.

Q: Find the perimeter of a pentagon with vertices M (-1,6), N (3, 6), P (6, 4), Q (6, 1) and R (4, 4).…

A: To find the perimeter of the pentagon

Q: Could a polyhedron exist with the given number of faces, vertices, and edges? Drag "yes" or "no" to…

A: there are given faces, vertices and edges. we have to find which polyhedron exists. we know the…

Q: Prove that quadrilateral PLUS with the vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle.

A: 1) Opposite sides are equal , 2) The diagonals of a rectangle are equal.  Distance formula of point…

Q: Could a polyhedron exist with the given number of faces, vertices, and edges? Drag "yes" or "no" to…

A:

Q: Prove that quadrilateral PLUS with the vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle.…

A:

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: A parallelogram has exactly two paris of perpendicular sides True or false ?

A: The rectangle has exactly two pairs of perpendicular sides.

Q: Both a parallelogram and a kite have two pairs of congruent sides. How are the congruent sides of a…

A:

Q: A polyhedron has 9 faces and 21 edges. How many vertices does it have ?

A: A polyhedron has 9 faces and 21 edges. F=9 and E=21. The objective is to find the number of vertices…

Q: If all perpendicular bisectors of all three segments of the following triangle are drawn, where will…

A: We know that, The circumcenter of a triangle is the point of intersection of the perpendicular…

Q: Calculate the perimeter of the triangle formed by the following set of vertices. {(-3, 1) , (3, 4) ,…

A: Given:       Vertices of triangle -3,1 , 3,4 , -1,-3       For perimeter of triangle , we have to…

Q: 6. Prove that two quadrilaterals are congruent if a side, angle, side, angle, side of one are equal…

A: This can be proved by using the definition of congruence. Two figures or objects are congruent if…

Q: 5. Suppose AABC is a triangle and l is a line such that none of the vertices A, B, or C lies on l.…

A: Find your answer below

Q: A polyhedron has 12 faces and 30 edges. How many vertices does it have ?

A: Given,            A polyhedron has 12 faces and 30 edges.

Q: A convex quadrilateral has 2 diagonals. A convex pentagon has 5 diagonals. If a convex polygon has…

A: To find the no. Of sides of a convex polygon with 324 sides.

Q: 1. Show that (2, 1, 6), (4, 7, 9) and (8, 5, -6) are the vertices of a right triangle by finding the…

A:

Q: Is there a regular polygon with 8 diagonals? If so, how many sides does it have?

A: We have to find number of sides in regular polygon if possible where number of diagonals are 8. We…

Q: Calculate the perimeter of the triangle formed by the following set of vertices.…

A:

Q: 9. A polyhedron (not regular) has 14 vertices and 21 edges. How many faces must it have?

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Q: A solid in the formof a cube of edge 12 cm. is melted and formed into three smaller cubes of…

A:

Q: If a perpendicular bisector of all three segments of the following triangle are drawn, where will…

A: Solution:

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 the midpoints of the sides of a quadrilateral of the mice are vertices of a…

A: We need to prove the midpoints of the sides of a quadrilateral of are vertices of a parallelogram.…

Q: Determine the area of the triangle with vertices (9, 1, 6), (9, 1, 7), and (12, 1, 7).

A: Let the given vertices be A=9,1,6, B=9,1,7, C=12,1,7. Find the area of the triangle. The formula to…

Q: Calculate the perimeter of the triangle formed by the following set of vertices. {(0,0), (4, 4),…

A: .

Q: 1) How many triangles can be drawn on a plane using 8 non-collinear points?

A:

Q: A polyhedron (not regular) has 10 vertices and 6 faces. How many edges does it have? edges

A:

Q: Could a polyhedron exist with the given number of faces, vertices, and edges? Drag "yes" or "no" to…

A: We solve the question by using Euler's formula F + V - E=  2, where F is the number of faces, V the…

Q: Calculate the perimeter of the triangle formed by the following set of vertices. {(5, 4),(3,6),…

A: We have to find the parameter of the triangle formed by the vertices 5,4,3,6,7,8.

Q: Calculate the perimeter of the triangle formed by the following set of vertices. {(5, 4), (3, 6),…

A:

Q: 2. Show that if two sides of a cyclic quadrilateral are parallel, then the other two sides are of…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the area of the triangle with vertices P(4,10,7), Q(−1,4,1) and Q(3,7,2).

A:

Q: A polyhedron (not regular) has 11 vertices and 9 faces. How many edges does it have?

A: We have to find edges

Q: When three squares are joined at their vertices to form a rght triangle, the combined area of the…

A: answer of given question is in step 2

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: If a triangle is a complete 3-point, a quadrangle is a complete 4-point, a trilateral is a complete…

A: Given A triangle is a complete 3-point, quadrangle is a complete 4-point, a trilateral is a complete…

Q: Quadrilateral ABCD is considered a cyclic quadrilateral because there is a circle passing through…

A: for a cyclic quadrilateral the opposite angles are supplementary in nature that means the opposite…

Q: How many edges does a tetrahedron have ?

A:

Q: quadrilateral is cyclic if and only if a pair of its opposite angles are supplementary. True or…

A: A convex quadrilateral polygon in a plane is cyclic if, and only if, its opposite angles are…

Q: Prove that quadrilateral DAVE with the vertices D(2,1), A(6,-2), V(10,1), and E(6,4) is a mbus. Yt…

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

Q: Use Euler’s Formula to find the missing number of faces, edges, and vertices a) Faces = ?, Edges =…

A: Euler's formula is: F + V = E + 2, where F=the number of faces, V =the number of vertices, and E =…

Q: 27. Show that a triangle with vertices at (3, 5), (3, 2), and (2, 5) is a right triangle.

A: If we can prove that above triangle satisfies Pythagoras theorem then we can say that above triangle…

Q: A polyhedron (not regular) has 10 vertices and 7 faces. How many edges does it have?

A: Given that polyhedron has 10 vertices and 7 faces. We need to find the number of edges in the…

Q: The vertices of a quadrilateral are M(–1, 1), N(1, –2), O(5, 0), and P(3, 3). Which statement…

A: Given query is to find the shape of quadrilateral.

Q: If a student claims that all figures with four congruent sides are squares. would he be correct?

A:

Q: Calculate the perimeter of the triangle formed by the following set of vertices.…

A:

Q: How many side does a tetrahedron have ? How many number of edges which meet at a vertex does a…

A:

Q: Determine if quadrilateral EFGH with E(-2, 1), F(1, 2), G(4, 1), H(1, -4) is a parallelogram by…

A: Parallelogram is a quadrilateral with opposite side parallel and equal. So to check whether the…

Q: that if P, Q, R and S form a quadrilateral, then it cannot be cyclic.

A: A quadrilateral inscribed in a circle is known as a cyclic quadrilateral. so,  if a pair of…