In Exercises 19–22, find the area of the parallelogram whose vertices are listed.

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(8, 7,…

A:

Q: Show that the diagonals of a parallelogram are perpendicular if and only if it is a rhombus, i.e.,…

A: please find the attached solution

Q: Can you prove the quadrilateral is a parallelogram based on the given information? Explain. 11.

A: if the pair of opposite angle are equal then a quadrialteral is a parallelogram.

Q: In Exercises 5 and 6, use the glven Informatlon to write the standard equation of the circle. 5. The…

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

Q: Which figure represents the net of a triangular prism?

A:

Q: Find the coordinates of vertices of a unit cube where the three concrrent edges are the coordinte…

A:

Q: Find the area of a quadrilateral with vertices A( - 1 . - 1), 5(9, 4), C(20, 6).and D(10, 1).

A:

Q: Which information does not prove that quad. ABCD is a parallelogram? b. AD | BC; AD = BC a. AC and…

A: (a) If AC¯ and BD¯ bisect each other, then ABCD is a parallelogram.  (b) If AD¯∥BC;AD≅BC, then ABCD…

Q: In Exercises 3 and 4, list the sides of the given triangle from shortest to longest. 4. B115° 52° D

A:

Q: snip

A: Given Parallelogram vertex।  A(1,1,1,1)  B(2,3,4) C(6,5,2) , D(7,7,5) Area = ∥AB ×AD∥ AB =…

Q: e of the parallelepiped with the given vertices A, B, C and

A:

Q: Consider the quadrilateral y with vertices at M(0, 0), N(a, 0), P(a, b), and Q(0, b). Explain why…

A: Given figure is: Quadrilateral MNPQ has vertices M, N, P, Q with coordinates (0, 0), (a, 0), (a, b)…

Q: 2 Find the volume of the parallelepiped whose edges are represented by A=i-13j+ 4k, B = 31+2j-7k and…

A: Given A→=i-13j+4k,  B→=3i+2j-7k and C→=i-2j+2k

Q: In Exercises 23 and 24, find the exact areas of the shaded regions. 23. 24. A B 10 cm 10 cm 12 m D…

A: 23)  Equilateral triangle: If in triangle all three sides have same length then triangle is…

Q: Consider the triangular prism shown in Exercise 2. a) How many vertices does it have? b) How many…

A: A triangular prism is as shown below :

Q: The parallelogram (ABCD) has vertices at A(2,-1, 4), B(1,0, -1).C(1,2,3), and D, then

A: Let A(2,-1,4) , B(1,0,-1) , C( 1,2,3) and D(x,y,z) Let AC be one diagonal and BD be another…

Q: Prove that if DABCD is a parallelogram, then DABCD is convex.

A:

Q: Show that A(-3, 1), B(1, -1), C(4, 1), and D(3, 5) are vertices of a trapezoid.

A: Given vertices are A-3,1, B1,-1, C4,1 and D3,5. To show the vertices are of a trapezoid. Solution:…

Q: 3. Write the (a) center, (b) vertices, (c) covertices, (d) foci, (e) length of MA, and (f) length…

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

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

A:

Q: Find measures of the angles between the diagonals of the rectangle whose vertices are A = (1,0), B =…

A:

Q: Given a cyclic quadrilateral whose sides are 4 cm, 5 cm, 8 cm, and 11 cm. Its area is

A:

Q: Find the length of the longer diagonal in a rhombus with sides of length 12 and a smaller diagonal…

A:

Q: Find the area and the perimeter of a rhombus whose diagonals have lengths 18 in. and 24 in.

A: Given that the diagonal of rhombus is 18 in and 24 in To sketch the rhombus, Let “ABCD” be a…

Q: Show that the triangle with vertices A(0, 0), B(1, √2), andC(2, 0) is equilateral.

A: An equilateral triangle is a triangle in which all sides are equal, and consequently, all angles are…

Q: Verify that the points A(0, 3, 2), B(1, 5, 5), C(6, 9, 5), D(5, 7, 2) are the vertices of a…

A: Given points are A(0,3,2), B(1,5,5), C(6,9,5), D(5,7,2).

Q: Give the definition of a rhombus and prove that the area of a rhombus is half the product of the…

A: A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus,…

Q: In this exercise we find the area of a plane figure. Draw the parallelogram with vertices A(3, 5),…

A: Here we have to draw the parallelogram with vertex A(3,5), B(7,5), C(5,8), and D(9,8).  The graph of…

Q: 7. Find the measures of the hyperbolic angles of the Euclidean square with vertices (0, 1), (0, 2),…

A:

Q: In Exercises 13 and 14, find the length of the midsegment of the trapezoid with the given vertices.

A:

Q: What is the area of the parellelogram ABCD if the coordinates of the vertices are A (5,0), B (8,2),…

A: Explanation and solutions is given below....

Q: Find the perimeter of AABC with vertices A(2, 4), B(8, 12), and C(24, 0).

A: TO FIND PERIMETER OF ∆ABC FORMULAE USED 1) PERIMETER OF TRIANGLE = SUM OF ALL THE SIDES 2) DISTANCE…

Q: What is the most precise name for quadrilateral ABCD with vertices A(-1,0), B(4,0), C(5,4), and…

A:

Q: Verify that the points A(2, −3, 1), B(6, 5, −1), C(7, 2, 2), D(3, −6, 4) are the vertices of a…

A: Given: The points A2,-3,1, B6,5,-1, C7,2,2, D3,-6,4.

Q: 2. What is the perimeter of a rhombus with diagonals of 12 and 16 cm.?

A:

Q: Prove that a parallelogram is a rhombus, a parallelogram with four equal sides, if and only if its…

A: Given : ABCD is a parallelogram              AB≅BC              AC⊥BD Prove : ABCD is a rhombus

Q: Prove that the diagonals of any parallelogram bisect each other. (Hint: Label three of the vertices…

A: Given:- ABCD is a parallelogramTo prove:-AO=CO                 DO=BOProof:-In ∆AOD and ∆COB∡OAD=∡OCB…

Q: Find the length of a side of a rhombus whose diagonals 48 cm and 14 cm long. are

A: Given, The diagonals of the rhombus are 48 cm and 14cm long. In the rhombus CB= 48 cm and AD= 14 cm…

Q: Show that the triangle with vertices A(0, 0), B(1, √3), and C(2, 0) is equilateral.

A:

Q: Find the coordinates of the orthocenter of a triangle with vertices at each set of points on a…

A: Given that: (1, 5), (6, 10), (0, 16)

Q: What is the most precise name for quadrilateral ABCD with vertices A(-1,0), B(1,2), C(4,2), and…

A: We will use distance formula to find the sides and diagonal of quadrilateral.

Q: What is the most precise name for quadrilateral ABCD with vertices A(-5, 2), B(-3,4), C(5,4), and…

A: We have to check As per guideline we have to solve one question

Q: Prove that if ABCD is a parallelogram, then its diagonals bisect each other.

A: Let us consider a paralellogram ABCD which have diagonals AC And BD and intersect at point E

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(2,…

A: Given points, A(1,1,3) B(2,7,1) C(4,10,-6) D(3,4,-4) Let a,b,c,d, are position vectors of point…

Q: Write an indirect proof. 7. Given: mZ1 + mL2 Prove: AABC is not an isosceles triangle with vertex B.

A: The solution is :

Q: Consider this Platonic Solid, the cube:How many faces?  edges?  vertices?

A:

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: Plot the image of quadrilateral ABCD under a reflection across line . C D

A: Reflection is a transformation representing the flip of the figure. If we are reflecting a figure…

Q: Consider the quadrilateral with vertices at M(0, 0). N(a, 0), P(a + b. c), and Qlb, c). Explain why…

A: MN=a-02+0-02=aPQ=a+b-b2+c-c2=aMQ=b-02+c-02=b2+c2NP=a+b-a2+c-02=b2+c2 Clearly, MN=PQ  &  MQ=NP

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…