Any math majors or mathematicians?
- Thread starter Danycacks
- Start date
What do you need?
For now, I gotta prove that the diagonals on a rectangle are equal using congruent angles, alternate interior/exterior angles, the ASA, SSS, AAS theories and the pons asinorum (if thats how you spell it). Dont use the pythagorean theorem.
Shugg84
Banned
I think this is how you would do it. I don't know how to post images.
If you have the triangle
A B
C D
and a diagonal from AD and BC.
You know that AB = CD and AC = BD because it's a rectangle
Also using that Z angle theorem (can't remember what its called where you have two parallel lines and the angle going through it).. you know that <CDA = < DAB
<DCB = < CBA
Finally the last angle of each is a right angle so all the angles are equal and you have two sides are equal. Isn't that enough to show that they are congruent?
If you have the triangle
A B
C D
and a diagonal from AD and BC.
You know that AB = CD and AC = BD because it's a rectangle
Also using that Z angle theorem (can't remember what its called where you have two parallel lines and the angle going through it).. you know that <CDA = < DAB
<DCB = < CBA
Finally the last angle of each is a right angle so all the angles are equal and you have two sides are equal. Isn't that enough to show that they are congruent?
I think this is how you would do it. I don't know how to post images.
If you have the triangle
A B
C D
and a diagonal from AD and BC.
You know that AB = CD and AC = BD because it's a rectangle
Also using that Z angle theorem (can't remember what its called where you have two parallel lines and the angle going through it).. you know that <CDA = < DAB
<DCB = < CBA
Finally the last angle of each is a right angle so all the angles are equal and you have two sides are equal. Isn't that enough to show that they are congruent?
I used that but he said it didnt prove the diagonals were equal. I tried explaining that the diagonals create 4 triangles and that the one on the left and right side are isoceles and that would make them equal but now I have to prove theyre isoceles and I doubt this problem is THAT complicated...
Once you have the two triangles with two equal sides and both sharing the same angle (right angle). Can't you use this SAS (Side Angle Side postulate for proving congruent triangles ...) which proves that they are congruent and if they are congruent then the two diagonals must be equal as well
Greenhornet
A God Among Kings
too much english and not enough math you two are doing ... no good ... no good
wait this sounds like geometry, which math are they doing?
Megatron Island
Rookie
ok, using a rectangle abcd, and the intersection of the diagonals being E:
A. B
E
D. C
I used alt. Interior angles to prove
<Dac=<BCA
<adb=<cbd
You know from opposite sides that
AD=BC
So the two triangles in the inside ADE=BEC from the ASA postulate.
If those two angles are congruent, then their legs are as well, so
AE=EC=DE=EB
And that means for the diagonals:
AE+EC=AC
DE+EB=DB
Must also be equal?
Vertical angles are equal as well, maybe use that? It's been awhile since I did this lol.
Edit: fukk it, I have no idea lol.
A. B
E
D. C
I used alt. Interior angles to prove
<Dac=<BCA
<adb=<cbd
You know from opposite sides that
AD=BC
So the two triangles in the inside ADE=BEC from the ASA postulate.
If those two angles are congruent, then their legs are as well, so
AE=EC=DE=EB
And that means for the diagonals:
AE+EC=AC
DE+EB=DB
Must also be equal?
Vertical angles are equal as well, maybe use that? It's been awhile since I did this lol.
Edit: fukk it, I have no idea lol.
Megatron Island
Rookie
Double.