Question

Geometry A/ Please help

The options in the box are
36
6
72
right
acute
congruent
straight

Answer 1

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

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