Question 1: A kite has two pairs of adjacent equal sides. If one pair of equal sides measures 8 cm and the other measures 5 cm, what is the perimeter of the kite?

Answer: 26

Question 2: In a kite, the diagonals are perpendicular. If one diagonal measures 10 cm and the other measures 24 cm, what is the area of the kite?

Answer: 120

Question 3: A kite has one pair of equal angles at the vertices where the equal sides meet, measuring 40° each. Find the measure of the angles where the diagonals intersect, assuming the diagonals are perpendicular.

Answer: 100

Question 4: Construct a kite on the grid with sides 6 cm and 4 cm. Ensure the diagonals are perpendicular and one diagonal is 8 cm long. Describe the steps you take.

Answer: Construct the longer diagonal first, then use compass and straightedge to draw the shorter sides meeting at the ends, ensuring perpendicular diagonals.

Question 5: A real-world kite has a diagonal length of 15 cm and a height of 9 cm. If the diagonals are perpendicular, what is the area of the kite?

Answer: 67.5

Question 6: Calculate the length of the other diagonal in a kite if one diagonal measures 12 cm and it is known that the diagonals are perpendicular and the area is 84 cm².

Answer: 14

Question 7: Identify and explain the mistake in the following statement: 'All kites have four right angles.'

Answer: Incorrect because kites do not necessarily have right angles; only some special cases do.

Question 8: Given a kite with diagonals of 10 cm and 16 cm, where the longer diagonal is horizontal, find the length of the segment of the shorter diagonal between the intersection point and one vertex, assuming diagonals bisect each other and are perpendicular.

Answer: 8

Question 9: A kite's diagonals intersect at point O. If the diagonal of 18 cm is bisected at O and the segment from O to a vertex along the shorter diagonal is 7 cm, what is the length of the shorter diagonal?

Answer: 14

Question 10: A kite is formed with sides of 7 cm and 5 cm. The diagonals are perpendicular, with the longer diagonal measuring 12 cm. Calculate the length of the shorter diagonal.

Answer: 8

Question 11: Explain why the diagonals of a kite are always perpendicular, and discuss any exceptions to this property.

Answer: Diagonals are perpendicular because of the symmetry in kite properties; exceptions occur in special cases like rhombuses or squares.