Can anyone prove?

Question

Anyone please prove that the diagonals of a rectangle are equal using the theory of congruent triangles. Show the steps please.

Answer 1

let by ABCD =rectangle =>AB=CD & AD=BC &are parallels, Compare the triangle ABC with triangle DCB.
we have AB=CD, BC=CB,

Answer 2

First, notice that the top, one side, and one diagonal of the rectangle form a triangle; and the top, the other side, and the other diagonal form another. Since both trinagles use the top, we know that they have that side equal, and since the opposite sides of a rectangle are equal, we know that they have two equal sides. Notice now that the angle where these two sides meet are the top two corners of the rectangle, so we know that these angles are equal. Since we have side-angle-side, we can now say that the two triangles are congruent. That makes the diagonals corresponding sides of congruent triangles, so they are equal.

Answer 3

Draw the rectangle be ABCD.
Draw the two diagonals AC and BD.
Since the opposite sides of a rectangle are equal we have ;
AB = CD and AD ==BC
Since all right angles are equal, we have
angle DAB = angle CBA
Therefore triangle CBA congruent triangle DAB because of SAS
Therefore AC = BD because corresponding parts of congruent triangles are congruent.

Q.E.D

Answer 4

K.. i dont know how to put this in words but i'll try...

Let the triangle be ABCD with the point of intersection of diagonals O
1.) Draw the diagonals..
2.)Now there will be 4 triangles formed.
3.)Taking the triangles with the length as their base..
Angle AOB will be equal to angle COD(vertically opposite)
Length ab=length cd
and alternate angles ABO and DOC
Thus both triangles proved congurent with ASA (angle.side .angle)exiom of congurency

Repeat the same process with triangles COA and DOB..

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Cheers!

Answer 5

No, because mathematics is similar to a board game. Made up entertainment.