Question

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square

Answer 1

please mark as brainlist

Answer 2

Answer:

Given:

◻ABCD is a quadrilateral.

diag AC = diag BD, intersecting at E.

AC and BD are perpendicular bisectors of each other

∴ ∠E = 90o

To prove:

◻ABCD is a square.

Solution:

In △ABE and △ADE.

BE = DE ....given

AE ≅ AE ...common side

∠AEB ≅ ∠AED ....each 90o

∴ △ABE ≅ △ADE ...SAS test of congruence

∴ AB = AD ...c.s.c.t. ....(1)

Similarly, we can prove △ABE ≅ △CBE

∴ AB = CB ....c.s.c.t. ....(2)

And, △ADE ≅ △CDE

∴ AD = CD ....c.s.c.t. ....(3)

∴ From (1), (2) and (3),

AB = CB = CD = AD

∴ ◻ABCD is a square