Question 1: A rhombus has sides of length 8 cm. One of its diagonals measures 10 cm. Calculate the length of the other diagonal.

Answer: 12 cm

Question 2: In a rhombus, the diagonals intersect at right angles. If one diagonal is 14 cm and the diagonals bisect each other, find the area of the rhombus.

Answer: 98 cm^2

Question 3: Construct a rhombus with sides of 6 cm and diagonals of 8 cm and 10 cm. Show all steps in your construction.

Answer: Construction completed successfully with accurate bisecting diagonals.

Question 4: A rhombus has interior angles of 60° and 120°. Calculate the length of one side if the height (altitude) when the angle is 60° is 5 cm.

Answer: 10 cm

Question 5: Explain why the diagonals of a rhombus are perpendicular. Use reasoning based on properties of parallelograms and symmetry.

Answer: Diagonals bisect each other and are perpendicular because of the symmetry and the fact that a rhombus is a special type of parallelogram with equal sides and specific angle properties, resulting in perpendicular diagonals.

Question 6: A rhombus has diagonals of lengths 16 cm and 24 cm. Find the measure of each interior angle.

Answer: Each angle is 60° and 120°

Question 7: A real-world object is shaped like a rhombus with sides of 9 meters. Its diagonals measure 12 meters and 16 meters. Calculate the total length of the perimeter.

Answer: 36 meters

Question 8: Identify and correct the mistake: A student states that the diagonals of a rhombus are always equal in length.

Answer: The diagonals are not always equal; they are only equal in a square, not a general rhombus.

Question 9: Find the length of the side of a rhombus if its diagonals are 20 cm and 24 cm.

Answer: 13 cm

Question 10: Challenge: Prove that in a rhombus, the diagonals bisect the angles at the vertices.

Answer: Because the diagonals bisect each other and the sides are equal, the diagonals split the angles into two equal parts, which can be shown through geometric reasoning and properties of isosceles triangles formed.