Question

._.

Answer 1

oh wait, couldn't i just say

ABCD is a rhombus. Given.
Diagonals bisect interior angles. Property of a rhombus?

Answer 2

would that work, or is that too easy to be true

Answer 3

By sss similarity theorem \[\Delta ABC = {\Delta}ADC\]thus <ACB = <ACD

Answer 4

but this is straight out of the lesson

Answer 5

but how would that prove that the diagonals bisect the angles?

Answer 6

ooh i think i see what you mean

Answer 7

since this two angles <ACB and <ACD are congruent then we can conclude that half <BCD is equal to one of them.

Answer 8

Given, sides AB, AD, BC, and CD are congruent. Line AC = Line AC by the Reflexive Property. Triangles ABC and ADC are congruent by SSS. Angles ACB and ACD are congruent by CPCTC. Diagonal AC bisects Angle BCD by definition of an angle bisector.

would that be the whole thing or would i also have to prove that Diagonal BD bisects as well?

Answer 9

guys? :/

Answer 10

@hartnn do you know this?

Answer 11

diagnols means both, u need to do same thing in triangle ABD and BCD

Answer 12

sigh. ok, thanks :)

Answer 13

do i have to state the given information again?

Answer 14

nopes, once is enough

Answer 15

ok, just to make sure before i send it in. does this look right?

Given, sides AB, AD, BC, and CD are congruent. Line AC = Line AC by the Reflexive Property. Triangles ABC and ADC are congruent by SSS. Angles ACB and ACD are congruent by CPCTC. Diagonal AC bisects Angle BCD by definition of an angle bisector. Line BD = Line BD by the Reflexive Property. Triangles ABD and CBD are congruent by SSS. Angles ADE and CDE are congruent by CPCTC. Diagonal BD bisects Angle ADC by definition of an angle bisector. Therefore, the diagonals of the rhombus bisect the interior angles.

Answer 16

seems right.....don't u have an habit of numbering the equations?
in that way u could have used AB=AD=BC=CD ---->(1)
this at both places......

Answer 17

what do you mean?

Answer 18

how would you write it?

Answer 19

Given, sides AB, AD, BC, and CD are congruent.---->(1)
Line AC = Line AC by the Reflexive Property.------>(2)
From (1) and (2),
Triangles ABC and ADC are congruent by SSS.
Angles ACB and ACD are congruent by CPCTC.
Diagonal AC bisects Angle BCD by definition of an angle bisector.
Line BD = Line BD by the Reflexive Property.------>(3)
From (1) and (3),
Triangles ABD and CBD are congruent by SSS.
Angles ADE and CDE are congruent by CPCTC.
Diagonal BD bisects Angle ADC by definition of an angle bisector.
Therefore, the diagonals of the rhombus bisect the interior angles.

basically same thing, but does it *look* better ?

Answer 20

i guess, they just didn't teach it like that :/ i'm not sure if they would like that or not

Answer 21

then what you have written is complete.....u can use that

Answer 22

alright, thanks :)

Answer 23

welcome.