Prove a quadrilateral with vertices g(1,-1), h(5,1), i(4,3) and j(0,1) is a rectangle., using rectangle method 1.

Steps explained below.

Step-by-step explanation:

It is given that the vertices of the quadrilateral are G(1, -1), H(5, 1), I(4, 3) and J(0, 1).

A parallelogram is a rectangle if one of its angle is 90° (and therefore, all angles will be 90°).

A quadrilateral is a parallelogram if two pairs of opposite sides are equal.

So, lets prove GH = IJ, HI = GJ and H = 90°.

= 20

= 20

Therefore, GH = IJ

= 5

= 5

Therefore, HI = GJ

Two pairs of opposite sides are equal and hence GHIJ is a parallelogram.

Now, in Δ GHI,

= 25

Therefore, .

This shows that Δ GHI is a right angled triangle and ∠ H = 90°.

Hence, GHIJ is a rectangle.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.