Question

Please help , ayudame Por favor

Answer 1

Line segment AD

`AD = \sqrt{(c-0)^(2)+(d-0)^(2)}`

`AD = \sqrt{c^(2)+d^(2)}`

Line segment BC

`BC = \sqrt{[(b+c)-b]^(2)+(d-0)^(2)}`

`BC = \sqrt{c^(2)+d^(2)}`

Line segment AB

`AB = \sqrt{(b-0)^(2)+(0-0)^(2)}`

`AB = \sqrt{b^(2)+0^(2)}`

`AB = b`

Line segment CD

`CD = \sqrt{[c-(b+c)]^(2)+(d-d)^(2)}`

`CD = \sqrt{b^(2)+0^(2)}`

`CD = b`

Explanation:

We defined the length of each side by the Equation of the Line Segment, which is a particular case of the Pythagorean Theorem. Let
`A(x,y) = (0,0)`,
`B(x,y) = (b,0)`,
`C(x,y) = (b+c, d)` and
`D(x,y) = (c,d)`, we construct the equations below:

Line segment AD

`AD = \sqrt{(c-0)^(2)+(d-0)^(2)}`

`AD = \sqrt{c^(2)+d^(2)}`

Line segment BC

`BC = \sqrt{[(b+c)-b]^(2)+(d-0)^(2)}`

`BC = \sqrt{c^(2)+d^(2)}`

Line segment AB

`AB = \sqrt{(b-0)^(2)+(0-0)^(2)}`

`AB = \sqrt{b^(2)+0^(2)}`

`AB = b`

Line segment CD

`CD = \sqrt{[c-(b+c)]^(2)+(d-d)^(2)}`

`CD = \sqrt{b^(2)+0^(2)}`

`CD = b`