in rectangle ABCD:points J,K,L and M are the mid-points of sides AB,BC,CD and DA respectively: AB=24cm andAD=10cm . what kind of quadrilateral is JKLM?

Draw the diagonal BD and join the mid-points JM.

Consider the similar triangles ADB and AMJ. Can you prove that MJ (line joining mid-points of AD and AB) is parallel to DB?

Can you repeat with triangles CBD and conclude that MJ is parallel to LK?

Similarly can you prove that ML is parallel to JK?

What is the most precise name for quadrilateral ABCD with vertices A(-5, -1), B(-5, 3), C(-2, 3), and D(-2, -1)?

To determine the kind of quadrilateral JKLM is in rectangle ABCD, we need to examine its properties. Here's how you can approach this:

Step 1: Draw the rectangle ABCD and label the given points J, K, L, and M as midpoints of the respective sides.

Step 2: Recall the properties of midpoints in a rectangle. The segment connecting the midpoints of two sides of a rectangle is called a diagonal.

Step 3: Since JK is the diagonal connecting the midpoints of AB and BC, and LM is the diagonal connecting the midpoints of AD and CD, we can conclude the following:

- JK is a diagonal parallel to DC.
- LM is a diagonal parallel to BA.

Step 4: From the parallel lines property, we know that if two lines are parallel and a transversal intersects them, alternate interior angles are congruent.

Step 5: Consider the quadrilateral JKLM. By connecting JL and KM, we see that JL is parallel to KM based on the alternate interior angles. Additionally, JK is parallel to LM due to the properties of diagonals in a rectangle.

Step 6: As a result, we can conclude that JKLM is a parallelogram. A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

In summary, quadrilateral JKLM is a parallelogram.