Question 1: Define a kite in terms of its sides and angles. List two key properties that distinguish a kite from other quadrilaterals.

Answer: A kite is a quadrilateral with two pairs of adjacent sides equal. Key properties include: one pair of opposite angles are equal, and the diagonals intersect at right angles, with one diagonal bisected by the other.

Question 2: Construct a kite with two pairs of equal adjacent sides, each of length 5 cm and 7 cm. Ensure the diagonals intersect at right angles.

Answer: Students draw the kite on the grid with sides 5 cm and 7 cm meeting at the intersection point, ensuring the diagonals are perpendicular.

Question 3: In a kite, if one pair of equal adjacent sides measures 8 cm each, and the other pair measures 6 cm each, what is the perimeter?

Answer: Perimeter = 8 + 8 + 6 + 6 = 28 cm

Question 4: The diagonals of a kite measure 10 cm and 24 cm. If the shorter diagonal bisects the longer at right angles, find the lengths of the segments into which the shorter diagonal is divided.

Answer: Since the diagonals intersect at right angles and the shorter diagonal bisects the longer, each segment of the shorter diagonal is 5 cm.

Question 5: A kite has diagonals measuring 14 cm and 20 cm. If the diagonals intersect at right angles and the longer diagonal is bisected, what is the length of each half of the bisected diagonal?

Answer: Each half of the bisected diagonal is 10 cm.

Question 6: A real-world kite model has two pairs of equal adjacent sides measuring 9 cm and 12 cm. If the diagonals intersect at right angles, what is the area of the kite?

Answer: Area = (1/2) × diagonal1 × diagonal2; need diagonals to calculate area. If diagonals are 15 cm and 20 cm, area = 0.5×15×20=150 sq. cm.

Question 7: Given a kite with one diagonal of 16 cm and the other of 9 cm, the diagonals intersect at right angles, and the shorter diagonal is bisected. Find the length of the parts of the longer diagonal.

Answer: Using Pythagoras, the segments of the longer diagonal are each 8.5 cm.

Question 8: Prove that in a kite, the angles between the unequal sides are equal. Provide a brief explanation.

Answer: In a kite, the angles between the unequal sides are equal because they are formed by the pair of equal adjacent sides, which produce equal angles opposite each other.

Question 9: A student mistakenly claims that all diagonals of a kite bisect each other equally. Identify the error and correct it.

Answer: The error is that only one diagonal (the one connecting the vertices with equal angles) is bisected, while the other diagonal is not necessarily bisected. The correction is that only the diagonal connecting the vertices with equal angles is bisected.

Question 10: Challenge: In a kite, if the lengths of the two pairs of adjacent sides are 10 cm and 7 cm, and the diagonals are 15 cm and 20 cm, verify whether the diagonals can intersect at right angles.

Answer: Using the Pythagorean theorem, check if 15^2 + 20^2 = (diagonal segments)^2; since 225+400=625, the diagonals can intersect at right angles.