Answer:
Therefore,
[tex]AB=6\ unit\\BC=6\ unit\\CD=6\ unit\\DA=6\ unit\\[/tex]
Since , ABCD has four Right angles and four Congruent sides, it is a Square
Step-by-step explanation:
The four points for the Figure are
point A( x₁ , y₁) ≡ ( 0 , 6)
point B( x₂ , y₂) ≡ (6 , 6)
point C(x₃ , y₃ ) ≡ (6 , 0)
point D(x₄ , y₄ ) ≡ (0 , 0)
∠A = ∠B = ∠C = ∠D = 90°
To Prove:
ABCD is a Square
Proof:
∠A = ∠B = ∠C = ∠D = 90° .........Given:
Now By Distance Formula we have
[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
Substituting we get
[tex]l(AB) = \sqrt{(6-0)^{2}+(6-6)^{2})}=\sqrt{6^{2}}=6\ unit[/tex]
Similarly for BC ,CD ,DA we have
[tex]l(BC) = \sqrt{(6-6)^{2}+(0-6)^{2})}=\sqrt{(-6)^{2}}=6\ unit[/tex]
[tex]l(CD) = \sqrt{(0-6)^{2}+(6-6)^{2})}=\sqrt{(-6)^{2}}=6\ unit[/tex]
[tex]l(DA) = \sqrt{(0-0)^{2}+(6-0)^{2})}=\sqrt{6^{2}}=6\ unit[/tex]
Therefore,
[tex]AB=6\ unit\\BC=6\ unit\\CD=6\ unit\\DA=6\ unit\\[/tex]
Since , ABCD has four Right angles and four Congruent sides, it is a Square
