Prove that diagonals of square are perpendicular to each other
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Hello,
let's look at the figure.
Consider ΔAOD and ΔAOB.
we have that:
AD=AB because the slides of are equal;
OD=OB because the diagonals of a square bisect each other;
AO = AO because the common side.
Using congruency rules, we have:
ΔAOD ≡ ΔAOB
from which
∠AOD = ∠AOB
As
∠AOD + ∠AOB=180°
then
∠AOD = 90°;
that is:
AO ⊥ BD
Hence, AC ⊥ BD
bye :-)
let's look at the figure.
Consider ΔAOD and ΔAOB.
we have that:
AD=AB because the slides of are equal;
OD=OB because the diagonals of a square bisect each other;
AO = AO because the common side.
Using congruency rules, we have:
ΔAOD ≡ ΔAOB
from which
∠AOD = ∠AOB
As
∠AOD + ∠AOB=180°
then
∠AOD = 90°;
that is:
AO ⊥ BD
Hence, AC ⊥ BD
bye :-)
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