The perimeter of a kite is equal to the sum of the length of all of its sides.

The area of a kite is half the product of its diagonals.

The longer diagonal bisects the pair of opposite angles.

The longer diagonal bisects the shorter diagonal.

The diagonals are perpendicular to each other.

This is because the lengths of three sides of ∆CAD are equal to the lengths of three sides of ∆CBD. Here, diagonal 'CD' forms two congruent triangles - ∆CAD and ∆CBD by SSS criteria.

The longer diagonal forms two congruent triangles.

The sides AC and BC are equal and AD and BD are equal which form the two isosceles triangles. Here, diagonal 'AB' forms two isosceles triangles: ∆ACB and ∆ADB.

The shorter diagonal forms two isosceles triangles.

It has one pair of opposite angles (obtuse) that are equal.

A kite has two pairs of adjacent equal sides.

We can identify and distinguish a kite with the help of the following properties: Observe the following kite ACBD to relate to its properties given below. The longer diagonal of a kite bisects the shorter one. F 25 G X 16.5 Y E H XY = 16.5 = 33= 25 + a 8 = a so EH = 8Įxample-Midsegment (algebraic) Find the length of the midsegment.A kite is a quadrilateral that has two pairs of consecutive equal sides and perpendicular diagonals.

8 x 14 x = x = x = 11Įxample-Midsegment Find EH. S T M N R U |||| MN = (average of the parallel bases)Įxample-Midsegment Find x. Trapezoid Midsegment Theorem (6-6-6) The midsegment of a trapezoid is parallel to each base, and its length is one half the sum of the bases. Midsegment of a trapezoid Midsegment of a trapezoid-is the segment whose endpoints are the midpoints of the legs. Find the value of x so that ABCD is an isosceles trapezoid. W Z X Y kite properties

Theorem 6-6-4 If a trapezoid has one pair of congruent base angles then the trapezoid is isosceles. B C A D Given: ABCD is an isosceles trapezoid Then: < B < C < A < D Theorem 6-6-3 If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent. Isosceles Trapezoid Isosceles Trapezoid-a trapezoid with congruent legs (non-parallel sides) A B D C

Trapezoid Trapezoid-a quadrilateral with exactly one pair of opposite sides parallel A B D C Bases: parallel sides and Legs: non-parallel sides and Kite Example Find all the missing angles. Other Kite Observations -adjacent sides congruent -no parallel sides -1 pair opposite angles congruent -diagonals perpendicular -one diagonal bisects angles formed by adjacent sides -one diagonal is bisected -symmetry about one diagonal -two sets of congruent right triangles

Theorem 6-6-2 If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. Theorem 6-6-1 If a quadrilateral is a kite, then its diagonals are perpendicular. Kite Kite-a quadrilateral with exactly two pairs of consecutive sides congruent A B D C Properties of Trapezoids and Kites Geometry CP1 (Holt 6-6) K.

Kite properties