Using properties of kites :
Using properties of kites A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
Kite theorems :
Kite theorems Theorem
If a quadrilateral is a kite, then its diagonals are perpendicular.
AC BD
Kite theorems :
Kite theorems Theorem
If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.
A ≅ C, B ≅ D
Ex. 4: Using the diagonals of a kite :
Ex. 4: Using the diagonals of a kite WXYZ is a kite so the diagonals are perpendicular. You can use the Pythagorean Theorem to find the side lengths.
WX = √202 + 122 ≈ 23.32
XY = √122 + 122 ≈ 16.97
Because WXYZ is a kite, WZ = WX ≈ 23.32, and ZY = XY ≈ 16.97
Ex. 5: Angles of a kite :
Ex. 5: Angles of a kite Find mG and mJ
in the diagram at the
right.
SOLUTION:
GHJK is a kite, so G ≅ J and mG = mJ.
2(mG) + 132° + 60° = 360°Sum of measures of int. s of a quad. is 360°
2(mG) = 168°Simplify
mG = 84° Divide each side by 2.
So, mJ = mG = 84° 132° 60°