Question

Geometry A/ Please help

Answer 1

Answer:

Therefore,

$AB=6\ unit\\BC=6\ unit\\CD=6\ unit\\DA=6\ unit$

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

$l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}$

Substituting we get

$l(AB) = \sqrt{(6-0)^{2}+(6-6)^{2})}=\sqrt{6^{2}}=6\ unit$

Similarly for BC ,CD ,DA we have

$l(BC) = \sqrt{(6-6)^{2}+(0-6)^{2})}=\sqrt{(-6)^{2}}=6\ unit$

$l(CD) = \sqrt{(0-6)^{2}+(6-6)^{2})}=\sqrt{(-6)^{2}}=6\ unit$

$l(DA) = \sqrt{(0-0)^{2}+(6-0)^{2})}=\sqrt{6^{2}}=6\ unit$

Therefore,

$AB=6\ unit\\BC=6\ unit\\CD=6\ unit\\DA=6\ unit$

Since , ABCD has four Right angles and four Congruent sides, it is a Square