Question 1: In a kite, the diagonals are perpendicular. If one diagonal measures 8 cm and the other measures 6 cm, find the area of the kite.

Answer: 24 cm^2

Question 2: A kite has two pairs of adjacent equal sides. If the lengths of the equal sides are 5 cm and 7 cm, and the diagonals intersect at right angles, what is the length of the diagonal connecting the vertices with sides 7 cm?

Answer: 8 cm

Question 3: Construct a kite where two adjacent sides are 4 cm and 6 cm, and the diagonals are perpendicular. Use the grid to accurately draw the kite.

Answer: Student draws accurately on grid

Question 4: Calculate the measure of the angles between the equal sides in a kite where each pair of equal sides is 5 cm, and the diagonals are perpendicular.

Answer: 90 degrees

Question 5: If the diagonals of a kite are 10 cm and 24 cm, and they intersect at right angles, what is the length of the segment connecting the vertices with equal sides of length 6 cm?

Answer: 12 cm

Question 6: A designer is creating a decorative kite with two pairs of equal sides. The longer sides are 9 cm, and the shorter sides are 4 cm. Using the grid, construct an accurate sketch of this kite with perpendicular diagonals.

Answer: Student sketch on grid

Question 7: Determine the length of the diagonals if they are perpendicular, and the area of the kite is 36 cm^2, with one diagonal measuring 9 cm.

Answer: Diagonal 1: 9 cm, Diagonal 2: 8 cm

Question 8: In a kite, the diagonals are perpendicular. If one diagonal measures 10 cm, and the other is 6 cm, what is the length of the side connecting the vertices of the two equal sides?

Answer: 8 cm

Question 9: A kite has sides of 5 cm and 8 cm. The diagonals intersect at right angles, with one diagonal measuring 12 cm. Calculate the length of the other diagonal.

Answer: 9 cm

Question 10: Identify and correct the mistake in the following statement: 'All kites have four equal sides and two pairs of equal angles.'

Answer: Kites do not necessarily have four equal sides; they have two pairs of adjacent equal sides.

Question 11: A kite's diagonals intersect at right angles, and one diagonal measures 14 cm. If the area of the kite is 98 cm^2, find the length of the other diagonal.

Answer: 14 cm

Question 12: Explain why the diagonals of a kite are perpendicular and how this property can be used to prove that certain angles are equal.

Answer: Diagonals are perpendicular because of kite symmetry; this property helps prove angles between equal sides are equal.