Question

PLS HELP!!!
Prove the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.

Use the Distance Formula to find DE, EF, FG, and GD.

https://dlap.gradpoint.com/Resz/~yUA6AAAAAAgIra5N3YpQtB.zpl3LttmVT9xim0H2FDI5B/7234256,14D/Assets/questions/quiz/geometry/geocoorp/geocoorp-h-2.png

Answer 1

yikes

any attempts so far? it's just plugging stuff into the distance formula which unfortunately is a lot of algebra

if it's any help, DE and FG should be congruent; EF and DG should also be congruent

Answer 2

how should I use the Distance Formula for 4 pairs?

Answer 3

well you'd just do one at a time, for example, for DE you would just plug points D and E into the distance formula

D = (-a-b,c)
E = (0,2c)

distance formula = \[\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}=?\]

Answer 4

D = (-a-b,c)
E = (0,2c)

means we can let D be our point1 and D be our point 2

x1 = -a-b and x2 = 0
y1 = c and y2 = 2c

distance formula = \[\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}=?\]

\[\sqrt{(0-(-a-b))^{2}+(2c-c)^{2}}=?\]

remember pemdas, start from the inside of parentheses and work your way outwards

Answer 5

Pink
Elephants
March
Down
A
Street

:3

Answer 6

@Vocaloid for DE, -4 and c?

Answer 7

-4? hm.

what do you get for (0-(-a-b))^2?

Answer 8

-a-b=2?

Answer 9

so, 2 to the 2nd power, is 4?

Answer 10

start from the inside of the parentheses and work your way out

0 - (-a-b) = ?

remember we are not given any values for a and b so your solution should include a and b somewhere

Answer 11

so, 4ab?

Answer 12

i'm not really sure where you're getting 4 from haha

0 - (-a-b)

distribute the negative sign to get

a + b

therefore

(0-(-a-b))^2 = (a+b)^2

Answer 13

then you have (2c-c)^2 = c^2

so the distance is sqrt( [a+b]^2+c^2])

can't simplify further than that because you are not given any values for a, b, or c

anyway I gtg but you would repeat the same process for the three other segments