22. In parallelogram ABCD, E and F are the midpoints of AB and CD, respectively. Prove that AECF is a parallelogram.

Q: Every rectangle is a parallelogram. O True OFalse

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

Q: Given W(-1,5,2), X(6,-2,3) and Y(-2,-7,-3), are points in 3D, then determine the area of…

A: To find the area of the parallelogram formed by two vectors

Q: Label the numbers in the Venn Diagram: 1 2 2 (3 Parallelogram 1. 1 Square 2. 2 Rectangle 3. 3 4. 4…

A: 1= Parallelogram

Q: Prove that triangle ABC, which has vertices 4(3.4), B(5,-2), and C(1,-2) is isosceles. А (3,4) 4 3 2…

A: The given vertices of the triangle are  A(3, 4) B(5, - 2) C(1, - 2)

Q: 5A. In quadrilateral ABCD, ∠B=∠D, ∠B= (2x+5)°, ∠A=3x and x=35°, prove that ABCD is a parallelogram.

A: We need to prove that ABCD is parallelogram.

Q: 14a. Show that quadrilateral ABCD is a parallelogram Given A(2, 0) * B * (3, 4) , C(- 2, 6) and D(-…

A: Explanation of the solution is given below...

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

A: The given triangle JKLM is,

Q: Try to move the purple points of Parallelogram ABCD so that the midpoints of AC & BD are different.…

A: In a parallelogram the diagonals bisect each other i.e. the midpoints are same point.

Q: 1. If the bisectors of angles of a quadrilateral enclose a rectangle, then show that it is a…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: 9. Prove, by coordinate geometry that QRST is a parallelogram. Q(0

A:

Q: Given quadrilateral WXYZ with coordinates W(4, 5), X(9, 4), Y (8,0) and Z(3, 1). Prove or disprove…

A: Quadrilateral is parallelogram if diagonals bisect each other

Q: Let points A; B , C , and D in R3 have respective coordinates (1, 2, 3), (−2, 3, 5), (0, 3, 6), and…

A: Given: A(1, 2, 3), B(−2, 3, 5), C(0, 3, 6), D(3, 2, 4)

Q: 3. Juan used the theorem that states "the diagonals of a parallelogram bisect each other" to…

A: 1st option is correct.   Diagonals of parallelogram are AC and BD . O is the point of intersection…

Q: A(-3, 2), В(5, — 4), С(7, 7)

A: Consider the given points,  Now, prove that C is on the perpendicular bisector of segment…

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: 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 if DABCD is a parallelogram, then DABCD is convex.

A:

Q: 17. In parallelogram ABCD, if ED = 7x-213 and BD = 16x- 38, find BD. %3D B. C

A: Property of parallelogram:   The diagonals of parallelogram bisect each other. (17).  Using this…

Q: Find the of the triangle area with verfices Pl2,2,0), Q(13,-1) and R(-4,2,1)

A:

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: Prove that ABCD with vertices 4(-1,3), B(-4,-1), C(1,-1), and D(4,3) is a rhombus assuming it is…

A:

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: Find an eguaton for the set of all points (a sy, z) equiditant fom point (1,0,2) and

A:

Q: Let A= (−4,5,−4),B= (−5,2,−5),C=(−8,4,−7), and D= (−7,7,−6). Find the area of the parallelogram…

A:

Q: 2. Determine the value of each variable for parallelogram INDY that has diagonals that intersect at…

A:

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

A:

Q: J(5. -1), K(8, 2). L(11, 10), M(8, 7)

A:

Q: Show that the quadrilateral with the given vertices is a parallelogram. E(-5,-2), F(-3, 3), G(3, 5),…

A:

Q: ABCD is a parallelogram with A (0,0), B(2,4), and C (10,4). Find the possible coordinaes of D. 10…

A:

Q: Find the area of the parallelogram that has u = (1, 3, 0) and v = (−1, 0, 2) as adjacent sides.

A: Now cross product is,

Q: Prove that all the points on a perpendicular bisector of a line segment AB are equidistant from the…

A: Statement:All the points on a perpendicular bisector of a line segment AB are equidistant from the…

Q: can a given line be in a two planes?in ten planes?

A: Yes,             The given statement is true;     A line can be drawn in a two planes ;…

Q: Let A, be the center of the square inscribed in acute triangle ABC with two vertice side BC (as…

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: 11. Determine if the statement is true or false. "A kite is a parallelogram"

A: Given the statement, "A kite is a parallelogram"

Q: Show that if a line is drawn from the vertex of an isosceles triangle that bisects the base of the…

A: Let ABC is an isosceles triangle such that AB=AC. Let AD is the bisector of angle A. To prove BD=BC…

Q: 14 12 10 PARK 4. 2. 2. 10 12 14 00

A: By using the opposite sides parallel and conjugate theorem we show that the polygon which represent…

Q: Consider the points A(3, –1,2), B(2, 1,5) and C(1,–2, –2) Find the area of parallelogram ABCD with…

A: Given points  A(3,-1,2) B(2,1,5) C(1,-2,-2)

Q: Show that quadrilateral RSTV with vertices R(- 5, - 3), S(1, – 11), T(7, -6), and V(1, 2) is a…

A: Solution: Consider the given that RSTV has vertices R(-5, -3) , S(1, -11), T(7, -6), and V(1, 2)…

Q: 2. The diamond in a deck of playing cards is a rhombus. What does that mean about its diagonals?

A:

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: Prove analytically that the perpendicular bisector of the sides of a triangle are concurrent.

A:

Q: A parallelogram with congruent diagonals is a______?

A: A parallelogram has the following properties: Opposite sides are parallel and congruent.Opposite…

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: The vertices of quadrilateral PQRS form a square P(0, 0), Q(4, 3), R(7, -1) and S(3, -4). Use…

A: locating the points on the graph we get

Q: Suppose that A, B, C, D and A′, B′, C′, D′ (in those orders) form the vertices of convex…

A: Consider the given: Given:AB=A'B'In a parallelogram, parallel sides have equal length.In…

Q: A diagonal may be inserted onto a diagram of a parallelogram to complete a proof involving the…

A: A parallelogram is a closed figure with 2 pairs of opposite sides parallel to each other.