Purchase Solution

Four midpoints of any quadrilateral form a parallelogram.

Not what you're looking for?

Ask Custom Question

How can one prove that the 4 midpoints of the four sides of any quadrilateral form the vertices of a parallelogram using graph geometry (ie. x1, y1 etc. to denote the four vertices)?

Purchase this Solution
Solution Summary

Algebraic proof that the four midpoints of the four sides of any quadrilateral form the vertices of a parallelogram.

Solution Preview

Label the 4 corners of the quadrilateral
(x1,y1), (x2,y2), (x3,y3), (x4,y4),

Note the four midpoints can be connected to make a new quadrilateral, but is it a parallelogram? If it is, then the slopes of the lines of opposite sides have identical ...

Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Synthetic and analytical proof: parrallelogram

    582307 Synthetic and analytical proof: parrallelogram Theorem: If the consecutive midpoints of the sides of a parallelogram are joined in order, then the quadrilateral formed from the midpoints is a parallelogram. A.

  • Maltitudes, Circumcircles and Circumcenters

    Generally the four maltitudes of a quadrilateral are not concurrent, but if the quadrilateral is cyclic they are.

  • Line Intersections

    If P, Q are the midpoints of AB, CD respectively prove that i) AC + BD = 2PQ ii) AC+BC+AD+BD=4PQ ABCD is a quadrilateral. The midpoints of AB, BC, CD and DA are P,Q,R and S. Prove PQRS is a parallelogram.

  • inheritance hierarchy

    The private instance variables of Quadrilateral should be the x-y coordinate pairs for the four endpoints of the Quadrilateral. Write a program that instantiates objects of your classes and outputs each object's area (except Quadrilateral).

  • Proofs : Quadrilaterals

    Solution: Consider the quadrilateral ABCD in which We have to prove that ABCD is a parallelogram. Draw AC Now, we have two triangles. We know the sum of the angle measures of a triangle is 180 .

  • To prove a given quadrilateral a parallelogram

    Hence AMCN is a parallelogram. This solution gives a step by step procedure to prove a given quadrilateral, with some geometric conditions satisfied, is a parallelogram.

  • Finding the values of the sides of a parallelogram.

    4809 Finding the values of the sides of a parallelogram. Find the value of each variable in the parallelogram. 2z+1 4w 4z-5 w+3 By definition, a parallelogram is defined by a quadrilateral with opposite sides parallel and equal.

  • Angles in Polygons

    true 1- a square is also a rectangle - True 2- a parallelogram is also a trapezoid - False 3- a square is also a rhombus - True 4- a quadrilateral is also a parallelogram - Sometimes True Angles in polygons are investigated.

  • Geometry : Construction and Conjecture - What kind of quadrilateral is ACBD?

    (6) (4)+(5)-(6) (7) Thus (8) So the parallelogram ACBD is indeed a rectangle. A quadrilateral are investigated. The kind of quadrilateral is ACBD is determined. Equidistant from angles are examined.

View More Related Solutions