Anyone who answers this will get brainliest
show that diagonals of a square are equal and bisect each other

Proof is given below.

Step-by-step explanation:

Given:

ABCD is a Square.

i.e AB = BC = CD = DA

To Show:

Diagonals of a square are equal and bisect each other.

1.  AC = BD

2. AO = CO and   BO = DO

Proof:

ABCD is a Square  ............{Given}

∴ AB = BC = CD = DA ...........{All sides are equal of a Square ( 1 )}

∴ m∠ A = m∠ B = m∠ C = m∠ D = 90° ..{Measure of each vertex angle is 90° ( 2 )}

Now ,In  Δ ADC and Δ BCD

AD ≅ BC     ……….{From ( 1 )}

∠ ADC ≅ ∠ BCD = 90°     …………..{ From ( 2 )}

DC ≅ DC      ……….{Reflexive Property}

Δ ADC ≅ Δ BCD ….{Side-Angle-Side test}

∴ ∠ DAC≅ ∠ CBD...{corresponding angles of congruent triangles (c.p.c.t)( 3 )}

∴ AC ≅ BD  ......{corresponding sides of congruent triangles (c.p.c.t) }

∴ AC ≅ BD  ..... Proved ( 1 ) Diagonals are Equal

Now,In  Δ AOD and Δ BOC

∠ DAO ≅ ∠ CBO     …………..{From ( 3 ) c.p.c.t}

∠ DOA ≅ ∠ COB       ……….{Vertically Opposite Angles}

AD ≅ BC     ……….{From ( 1)}

Δ AOD ≅ Δ BOC ….{ by Angle-Angle-Side test}

∴ AO ≅ OC  ......{corresponding sides of congruent triangles (c.p.c.t) }

∴ DO ≅ BO  ......{corresponding sides of congruent triangles (c.p.c.t) }

i .e Diagonal bisect each other....... Proved..

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.