Question

Which statement proves that quadrilateral JKLM is a kite?

A. ∠M is a right angle and MK bisects ∠LMJ.
B. LM = JM = 3 and JK = LK = √17.
C. MK intersects LJ at its midpoint.
D. The slope of MK is –1 and the slope of LJ is 1.

Answer 1

A quadrilateral is a kite if the diagonals are:

i) perpendicular
ii) bisect each other
iii) not equal ( together with conditions i and ii this would make the quadrilateral a square)


Another definition of the kite is :

a quadrilateral with 2 pairs of equal adjacent sides.


Let's check the choices one by one:

A. ∠M is a right angle and MK bisects ∠LMJ.

according to these, ML and MJ may well be not equal...


B. LM = JM = 3 and JK = LK = √17.

this makes the quadrilateral a kite.


C. MK intersects LJ at its midpoint

if they are not perpendicular, the quadrilateral is not a kite.


D. The slope of MK is –1 and the slope of LJ is 1.

this only means that MK and LJ are perpendicular, but not whether they bisect each other,


Answer: only B

Answer 2

The statement that proves that quadrilateral JKLM is a kite is:

B. LM = JM = 3 and JK = LK = √17.

Let's understand what a kite is.

What is a kite?

A kite is known to be a quadrilateral that have four sides with each two pairs that are equal in length adjacent to each other.

This makes kite different from a parallelogram which has four sides and each two pairs are equal but they opposite to each other instead of adjacent.

Quadrilateral JKLM is a kite because we can see that option shows us that:

LM = JM = 3 (the two pairs that are adjacent and equal in length)

JK = LK = √17 (the two pairs that are adjacent and are equal in length).

Learn more about quadrilateral on https://brainly.com/question/8823615