Question

A kite is a quadrilateral with exactly two pairs of congruent consecutive sides. prove that quadrilateral jklm with vertices j(1, 5), k(4, 2), l(1, −4), and m(−2, 2) is a kite, and find its area.

Answer 1

A kite is a quadrilateral with two pairs of congruent consecutive sides. To prove that quadrilateral JKLM is a kite, you can show that opposite sides are congruent and one pair of opposite angles are congruent. The area of the kite can be found by dividing it into two triangles and calculating their areas.

Step-by-step explanation:

A kite is a quadrilateral with exactly two pairs of congruent consecutive sides. To prove that quadrilateral JKLM is a kite, we can show that opposite sides are congruent and one pair of opposite angles are congruent.

Step 1: Calculate the lengths of all four sides of the quadrilateral using the distance formula.

Step 2: Show that opposite sides are congruent by comparing their lengths.

Step 3: Show that one pair of opposite angles are congruent by calculating their measures using the slope formula.

To find the area of the kite, divide it into two triangles. Use the coordinates of the vertices to calculate the lengths of the diagonals. Then, use the formula for the area of a triangle to find the area of each triangle. Finally, add the two areas together to find the total area of the kite.