Question

what is a good plan for the question "quadrilateral ABCD has vertices A(3,4), B(-1,2), C(-3,-4) and D(5,-6). Verify that the quadrilateral formed by joining the midpoints of the sides of quadrilateral ABCD is a rhombus."?

Answer 1

open that and lets walk through it...

Answer 2

I would first plot your points...

Answer 3

i cant open it cause i dont have microsoft.

Answer 4

ok

Answer 5

so i just finished plotting it. what do i do next?

Answer 6

you must find the midpoints of all four sides
so you need midpoint of the following

AB
BC
CD
DA

Answer 7

When dealing with a rhombus, the definition and theorems are stated as ...


1. A rhombus is a parallelogram with four congruent sides.
While the definition states "parallelogram", it is sufficient to say: "A quadrilateral is a rhombus if and only if it has four congruent sides.", since any quadrilateral with four congruent sides is a parallelogram.

2. If a parallelogram has two consecutive sides congruent, it is a rhombus.

3. A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

4. A parallelogram is a rhombus if and only if the diagonals are perpendicular.

Answer 8

Label the midpoints as EFGH....that is what we have to prove is a rhombus

Answer 9

is that all i have to do?

Answer 10

so are numbers 1-4 that u said the steps of the plan then?

Answer 11

let me this easy. Okay-

Find the following
Find the midpoints as instructed above..label EFG
Distance of:
EF
EH
HG
FG

now find the slope of the opp sides...
so the slope of FG and EH should be the same (that proves they are parallel)
the slope of EF and HG should be the same

A rhombus has all 4 sides of equal length and opp sides are paralell lines.