Question

Refer to parallelogram ABCD to answer to the following questions. Multiple choice.

Answer 1

Let's look at the figure to deduce the coordinates of the points:

`A = (0,6),\quad B = (6,8),\quad C = (6,0),\quad D = (0,-2)`

Now recall the formula to compute the distance between two points
`P = (P_x, P_y), Q = (Q_x, Q_y)`:

`d(P,Q) = √((P_x-Q_x)^2 + (P_y - Q_y)^2)`

One diagonal is the distance between A and C, so the formula becomes

`d(A,C) = √((0-6)^2 + (6-0)^2) = √(36+36) = √(72) = 6√(2)`

Similarly, the other diagonal is the distance between B and D, so the formula becomes

`d(B,D) = √((6-0)^2 + (8-(-2))^2) = √(36+100) = √(136) = 2√(34)`

So, the lengths of the two diangonals are not the same

Answer 2

Option d. is correct

Explanation:

Parallelogram is a polygon with the following properties:

1. In parallelogram, opposite sides are equal

2. In parallelogram, opposite sides are parallel.

3. In parallelogram, opposite angles are equal.

4. In parallelogram, diagonals bisect each other.

Now, in this question, we need to choose one of the given options.

In parallelogram, diagonals are not always equal.

Rectangle and square are parallelograms in which diagonals are equal.

Rhombus is also a parallelogram but it's diagonals are not equal.

Therefore, we can say that in parallelogram, diagonals are not necessarily congruent .