Answer:
1) The correct options are;
- Two pairs of consecutive sides (but not all four sides) are congruent
- The diagonals are perpendicular
2) Yes, the quadrilateral meets the condition for the definition of a kite
Step-by-step explanation:
1) A kite has two pairs of adjacent equal sides, therefore a kite consists of two isosceles triangles adjacent to each other sharing the same base
Which shows that the diagonals which consists of the base of the two isosceles triangles and the bisector of the angles on the opposite sides of the common base of the isosceles triangles are perpendicular to each other
Therefore, the correct options are;
- Two pairs of consecutive sides (but not all four sides) are congruent
- The diagonals are perpendicular
2) The coordinates of the given quadrilateral are;
D = (-3, 4), A = (3, 6), B = (5, 0), C = (-2, -4)
Therefore, the length of DA = √((-3 - 3)² + (4 - 6)²) = 2·√10
the length of AB = √((5 - 3)² + (0 - 6)²) = 2·√10
The length of DC = √((-3 - (-2))² + (4 - (-4))²) = √(65)
The length of CB = √((-2 - 5)² + (-4 - 0)²) = √(65)
Therefore, the figure has two pairs of congruent consecutive sides but not all four sides
The slope of the bisector CA = (6 -(-4))/(3 - (-2)) = 2
The slope of the bisector DB = (0 - 4)/(5 - (-3)) = -0.5 = -1/2
Therefore, the diagonals are perpendicular which shows that the quadrilateral meets the condition for the definition of a kite.
