Question

Select the correct answers from each drop-down menu. Complete the steps in the proof that show quadrilateral KITE with vertices K ( 0 , – 2 ) , I ( 1 , 2 ) , T ( 7 , 5 ) , and E ( 4 , – 1 ) is a kite. Using the distance formula, K ⁢ I = ( 2 − ( – 2 ) 2 + ( 1 − 0 ) 2 = 17 , K ⁢ E = , I ⁢ T = , and T ⁢ E = . Therefore, KITE is a kite because .

1. thanhcong
Since KI = KE and IT = IE, KITE is a kite, Kites are two sets of quadrilaterals with identical adjacent edges.
KE = √17
IT = 3√5
TE = 3√5

### What is a Kite?

A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry.
A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry.
The name “deltoids” can also refer to a deltoid curve, an unrelated geometric object that is occasionally studied in relation to quadrilaterals.
Kites are also known as deltoids. If a kite is not convex, it may alternatively be referred to as a dart.
So, the quadrilateral KITE’s vertices are K(0, -2), I(1, 2), T(7,5), and E. (4,-1).
Using the formula for distance:
KE = √(-1 – (-2))² + (4 – 0)² = √17
IT = √(5 – 2)² + (7 – 1)² = 3√5
TE = √(-1 -5)² + (4 – 7)² = 3√5
Therefore, since KI = KE and IT = IE, KITE is a kite, Kites are two sets of quadrilaterals with identical adjacent edges.
KE = √17
IT = 3√5
TE = 3√5