Question

Helpp

Answer 1

I made it in a word doc if I send a picture, will you be able to view it?

Answer 2

yes you can attach the document using the "Attach file" tool :)
http://prntscr.com/a5ybup

Answer 3

Thank you @imqwerty :)

Answer 4

np :)
that image is solution to other similar question tho it is helpful

well if you prove that ABCD is a parallelogram which is a rhombus then you just need to prove that all its sides are congruent

Answer 5

I think that the given diagram is not marked up correctly.

It should be AE = EC marked rather than those angles.

Answer 6

@Directrix can u help me

Answer 7

oh

Answer 8

i mean *quadrilateral
not parallelogram

Answer 9

no its alright we can do it in 11 steps :))
well we can't say that the quadrilateral is a rhombus just by stating that the diagonals are perpendicular, there are more things to concern
consider this case-
here ABCD has perpendicular diagonals but the sides are not congruent so its not a rhombus

Answer 10

alright so lets start with the proof

all information given to us->
\(\angle CED=right ~angle\)
\(AB \equiv CD\)
DB bisects AC at E
\(\angle DCA \equiv \angle BAC\)
\(\angle DEA\) =right angle

right?

Answer 11

we look at \(\Delta ABC \) and \(\Delta ADC\)
here
\(AC=AC\) (common side)
\(\angle DCA \equiv \angle BAC\) (given)
\(AB=DC\) (given)

so therefore \(\Delta ABD \equiv \Delta ADC\) by ASA theorem

so we can say that \(AD=BC\) by CPCT

\({\angle AEB= \angle DEC = 90 ~~~(vertically~opposite~angles)\\ ~ \angle BEC= \angle ADE =90}~~~(vertically~opposite~angles)\)

now look at \(\Delta BEC \) and \(\Delta ABE\)
here
\(EC=AE\) (because DB bisects AC at E)
\(BE=BE\) (common side)
\(\angle AEB = \angle BEC\) (both equal to 90 degrees )

so \(\Delta BEC \equiv \Delta ABE\) by ASA theorem

so \(AB=AC\) by CPCT

so \(AB=BC=CD=DA\)
all sides are congruent so ABCD is a rhombus

Answer 12

@SuperFly123 than you check your posted question in the past day to this your question i have wrote a proofe yestoday or before - try get it there please

Answer 13

we don't need to talk about diagonals if all the sides are congruent :)

Answer 14

some days ago i have replid an posted question like this to prove that a quadrilateral is rhombus - sorry than not you was who posted it

Answer 15

not exactly just on the question and the question was exactly like your posted here above

Answer 16

i will try than i wil can get it now - ok.?

Answer 17

Ok

Answer 18

How do i show all four are right angles?

Answer 19

Wait, they don't have to be in order

Answer 20

look at the document I tried to do it for you I'm not sure if its what you need...

Answer 21

You show that that they are right angles witht t

Answer 22

That little symbol

Answer 23

Kind of helpful the document , idk

Answer 24

So is it what you need?