A quadrilateral has 2 pairs of angle with equal measures and 4 sides of equal length. What is the name of the quadrilateral? A. parallelogram B. rhombus C. trapezoid D. rectangle

The correct answer is option D; Rhombus

Step-by-step explanation: Basically, all the four options are quadrilaterals, or a plane shape with four sides. However, not all four-sided plane shapes have the same properties, and hence each of them has its own unique name due to its unique features or properties. A rhombus has four sides that are equal in measurement, but not all its four angles are equal in measurement. Two pairs of angles are equal to each other, and these are the pair of opposite angles. Also, the opposite sides/lines are parallel and congruent to each other.

A rectangle has, two opposite sides parallel and congruent, but unlike a rhombus, not all sides measure the same length. Only two opposite sides have equal measurement. In a rectangle, all four angles are congruent and they all measure 90 degrees each.

A trapezoid has only two sides as being parallel, and the other two sides are not parallel. The two parallel sides are referred to as the bases.

A parallelogram also has two equal sides as being parallel to each other and the two opposite sides are also congruent, just like a rhombus. However, unlike a rhombus, a parallelogram does not necessarily have all sides congruent. The two opposite sides may be equal in measure just like in a rectangle, but the angles are not all equal like in a rectangle.

Therefore, only a rhombus satisfies the conditions outlined in the question namely;

Two pairs of angles with equal measures, and four sides of equal length.

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)