Calculate the measures of the unmarked angles of the kite KITE.
Hint
Which angles are equal in a kite?
Answer
m∠3 = 100°, m∠4 = 140°
Example 2
If the angles of a kite are all equal, what are their measures? Would the resulting shape fit into any of the other quadrilateral categories?
Hint
What properties would the diagonals have with equal angles?
Answer
All four angles would be 90° in measure. The resulting shape would be a kite, rectangle, rhombus, square, and parallelogram. Talk about an identity crisis.
Example 3
Is a parallelogram always a kite?
Hint
What do we know about consecutive sides of parallelograms?
Answer
No, a parallelogram is not necessarily a kite.
Example 4
Is a square always a kite?
Hint
Is a square a rhombus?
Answer
Yes
Example 5
A kite has a perimeter of 60 km with one side length of 20 km. What are the lengths of the other three sides?
Hint
Which sides have to be congruent? How do these sides relate to the perimeter?
Answer
10 km, 10 km, and 20 km
Example 6
Calculate the perimeter of the kite JKLM.
Hint
Use the Pythagorean Theorem. It has never failed you before, has it? (If it has, blame Pythagoras, not us.)
