Question

verify that the diagonals of a rhombus are not equal.​

Answer 1

Step-by-step explanation:

PROOF: A rhombus ABCD, AC & DB are diagonals.

In triangle DAB & triangle CAB

AD = BC ( opposite sides)

AB = AB ( common side)

And there are no other equal elements in these 2 triangles, for making the triangles congruent. Congruence criterion , which can be applied here is SAS .

SO, for applying SAS, <A = <B.

=> adjacent angles should be equal.

Since their sum = 180°

So, each angle = 90° ( if angles are equal)

In such case, Rhombus takes the shape of a Square.

And in this condition , triangles become congruent &

So, diagonals AC = BD ( corresponding parts of congruent triangles)…

[PROVED]

Answer 2

PROOF: A rhombus ABCD, AC & DB are diagonals. And there are no other equal elements in these 2 triangles, for making the triangles congruent. ... => adjacent angles should be equal.