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
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 QuestionsCan 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.
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?
(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 of∠B 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.
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.