Given that a shape is a parallelogram, which of the following is sufficient to state that it is also a rectangle?
a.
the opposite sides are of equal length.
b.
the diagonals are of equal length.
c.
the opposite sides are parallel.
d.
the diagonals bisect each other.

B.The diagonals are of equal length

Step-by-step explanation:

A parallelogram is a quadritaleral whose opposite sides are equal and also parallel to each other.

A parallelogram has equal and parallel opposite sides. And also it's diagonals bisect each other.

However , there is one sufficient condition which makes a parallelogram a rectangle. If the diagonals of the parallelogram are equal the parallelogram will be rectangle.

B.The diagonals are of equal length

Step-by-step explanation:

We are given that a shape is a parallelogram.

We have to find that statement which is sufficient to state that  it is also a rectangle.

From given shape we have

Opposite sides are equal and parallel.

Diagonals of parallelogram bisect to each other.

Diagonals of parallelogram are not equal in length.

Opposite angles are equal.

Properties of rectangle:

Opposite sides are equal and parallel.

Diagonals are equal and bisect to each other.

Each angles is equal to 90 degrees.

Therefore, if the diagonals  are equal then it is sufficient to state that is also  a rectangle.

B.The diagonals are of equal length

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.