Verify the following:(i) `(0, 7, 10)`, `(1, 6, 6)`and `(4, 9, 6)`are the vertices of an isosceles triangle.

Explanation

Let the `P(0,7,10), Q(1,6,6) and R(4,9,6)` are the given vertices.

Then,

`PQ = sqrt((1-0)^2+(6-7)^2+(6-10)^2) = sqrt(1+1+16)=sqrt18 = 3sqrt2 `

`QR = sqrt((4-1)^2+(9-6)^2+(6-6)^2) = sqrt(9+9+0)=sqrt18 = 3sqrt2 `

`RP = sqrt((4-0)^2+(9-7)^2+(6-10)^2) = sqrt(16+4+16)=sqrt36 = 6 `

So, `PQ = QR` and `PQ+QR gt RP`

So, given triangle is an isoceles triangle with `PQ` and `QR` as equal sides.