A kite is a quadrilateral that has actually 2 pairs of equal adjacent sides. The angles where the nearby pairs of sides accomplish are equal. There room two species of kites- convex kites and concave kites. Convex kites have all their inner angles much less than 180°, whereas, concave kites have at the very least one that the interior angles better than 180°. This web page discusses the properties of a convex kite.

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1.What room the properties of Kite?
2.Properties the the Diagonals that a Kite
3.Solved examples on nature of Kite
4.Practice concerns on properties Of Kite
5.FAQs on nature Of kite

What room the properties ofKite?


A kite is a square that has two pairs of consecutive equal sides and perpendicular diagonals. The much longer diagonal that a kite bisects the much shorter one. Observe the following kite ABCD to relate come its properties provided below.


(angle ABC)(angle BCD)(angle CDA)(angle DAB)Side ABSide BCSide CDSide ADDiagonal ACDiagonal BD

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We deserve to identify and distinguish a kite through the aid of the following properties:

A kite has two bag of surrounding equal sides. Here, AC = BCand ad = BD.It has one pair of opposite angles (obtuse) that are equal. Here, ∠A = ∠BIn the diagonal line AB, AO = OB.The much longer diagonal forms two congruent triangles. Here, diagonal 'CD' forms two congruent triangles -∆CAD and ∆CBD by SSS criteria. This is due to the fact that the lengths of three sides of∆CAD room equal come the lengths of three sides of∆CBD.The diagonals room perpendicular to every other. Here, abdominal ⊥ CD.The longer diagonal bisects the shorter diagonal.The longer diagonal bisects the pair of opposite angles. Here, ∠ACD = ∠DCB, and ∠ADC = ∠CDBThe sum of the internal angles that a dragon is equal to 360°.

Properties of the Diagonals the a Kite


As us have discussed in the earlier section, a kite has actually 2 diagonals. The vital properties of kites through respect to their diagonals are provided below.

The two diagonals space not of the exact same length.Thediagonals that a kite crossing each various other at appropriate angles. It have the right to be observed that the much longer diagonal bisects the much shorter diagonal.The shorter diagonal that a kite forms two isosceles triangles. This is since an isosceles triangle has two congruent sides, and a kite has actually two pairs of nearby congruent sides.

Challenging Questions

Can a dragon be dubbed a parallelogram?Can a kite have sides of 12 units, 25 units, 13 units, and 25 units?

Topics related to Properties that Kite

Check out part interesting write-ups related come the nature of a kite.

Important Notes

Some important points around a kite are provided below.

Akite is a quadrilateral.If the two nearby sides the a kite are labeled together 'side 1' and also 'side 2', then the perimeter of thekite is 2 (side 1 + side 2).The area the a kite is fifty percent the product ofits diagonals.

Example 1: observe the kite given below and also answer the adhering to questions:

(a) If abdominal = 7 units, what is the measure of AC?

(b) If CD = 13 units, what is the measure up of BD?

(c) If∠B = 118°, climate what is the measure up of∠C?

Solution:

(a) We recognize that 2 pairs of nearby sides that a kite room equal. In the dragon ABCD, abdominal muscle = AC and BD =DC. Due to the fact that the size of abdominal muscle is recognized to it is in 7 units, AC = 7 units.

(b) Also, because the length of DC is 13 units, the length of BD is additionally 13 units.

(c) as per the properties of a kite, one pair of the contrary angles space equal. In the dragon ABCD,∠B =∠C. Due to the fact that the measure ofB is recognized to be 118°,∠C is also equal come 118°.


Example 2: Find the area and also perimeter of the kite presented below, wherein side abdominal = 5 units, side BD = 26 units, AE = 10 units, ED = 24 units, be = 12 units, EC = 12 units.

Solution:

Given: the size of the horizontal diagonal BC = 12 + 12 = 24 units; and also the size of diagonal advertisement = 10 + 24 = 34 units.

The area the a kite = 1/2 × size of diagonal line 1 × length of diagonal 2. Therefore, the area the the kite = 1/2× 24× 34= 12× 34 = 408 square units.

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The perimeter that a kite= amount of the size of every sides the the kite. The political parties of the kite are AB, AC, BD, andDC. Native the kite, we observe that abdominal = 5 units, and from the properties of the kite, we recognize that nearby pairs that sides room equal. Therefore, indigenous the kite ABCD, abdominal = AC, therefore, AC is likewise equal come 5 units. Because BD = 26 systems DC is also equal to 26 units. Therefore, the perimeter the the dragon = abdominal + AC + BD + DC, i beg your pardon is same to 5 + 5 + 26 + 26 = 62 units.