The image shows a page from a mathematics exercise book focusing on parallelograms and rhombuses, with various questions related to their properties and calculations. I will translate and explain the questions one by one.

1. 选择题 (Multiple Choice Questions)

   • (每小题 4 分，共 24 分) Each question is worth 4 points, total 24 points.

   1. 矩形具有而一般平行四边形不具有的性质是 (The property that rectangles have but general parallelograms do not)

      • A. 对角线相等 (Diagonals are equal)
      • B. 对边相等 (Opposite sides are equal)
      • C. 对角相等 (Opposite angles are equal)
      • D. 对角线互相平分 (Diagonals bisect each other)

   2. 若 O 是四边形 ABCD 的对角线的交点, 且 OA = OB = OC = OD, 则四边形 ABCD 是 (If O is the intersection point of the diagonals of quadrilateral ABCD and OA = OB = OC = OD, then quadrilateral ABCD is)

      • A. 平行四边形 (Parallelogram)
      • B. 矩形 (Rectangle)
      • C. 四边形 (Quadrilateral)
      • D. 梯形 (Trapezoid)

   3. 已知四边形 ABCD, 下列条件中, 不能判定 ABCD 为矩形的是 (Given quadrilateral ABCD, the following conditions cannot determine ABCD as a rectangle)

      • A. ∠A = ∠B
      • B. ∠A = ∠C
      • C. AC = BD
      • D. AB ⊥ BC

   4. 如图, 在菱形 ABCD 中, AB = 5, ∠BCD = 120°, 则对角线 AC 的长度是 (As shown in the figure, in rhombus ABCD, AB = 5, ∠BCD = 120°, then the length of diagonal AC is)

      • A. 20
      • B. 15
      • C. 10
      • D. 5

   5. 如图, 在菱形 ABCD 中, AC = 8, BD = 6, 则△ABC 的周长是 (As shown in the figure, in rhombus ABCD, AC = 8, BD = 6, then the perimeter of △ABC is)

      • A. 14
      • B. 16
      • C. 18
      • D. 20

   6. 如图, 四边形 ABCD 的对角线 AC, BD 互相垂直, 则下列条件能判定四边形 ABCD 为菱形的是 (As shown in the figure, if the diagonals AC and BD of quadrilateral ABCD are perpendicular, then the following conditions determine that ABCD is a rhombus)

      • A. BA = BC
      • B. AC, BD 互相平分 (AC and BD bisect each other)
      • C. AC = BD
      • D. AB // CD (AB is parallel to CD)

2. 填空题 (Fill in the Blanks)

   • (每小题 4 分，共 16 分) Each question is worth 4 points, total 16 points.

   7. 如图, 在四边形 ABCD 中, 添加一个条件，使四边形 ABCD 是矩形 (As shown in the figure, add a condition to make quadrilateral ABCD a rectangle)

   8. 如图, 矩形 ABCD 的对角线 AC 和 BD 相交于点 O, 过点 O 的直线分别交 AD 和 BC 于点 E, F, AB = 2, BC = 3, 则图中阴影部分的面积为 (As shown in the figure, the diagonals AC and BD of rectangle ABCD intersect at point O, the line through point O intersects AD and BC at points E and F respectively, AB = 2, BC = 3, find the area of the shaded part)

   9. 已知菱形的一条对角线长为 24cm, 它的一条对角线长为 6cm, 则另一条对角线长为 (Given a rhombus with one diagonal of 24 cm and another diagonal of 6 cm, find the length of the other diagonal)

   10. 如图, 在菱形 ABCD 中, 点 E 是 BC 上一点, DF ⊥ AE, 垂足为点 F. AB = 3, AE = AD = 5, 则 AF 的长为 (As shown in the figure, in rhombus ABCD, point E is on BC, DF is perpendicular to AE with foot F. Given AB = 3, AE = AD = 5, find the length of AF)

Would you like help solving specific questions or need further details on any part? Here are five additional questions you might consider:

1. How do you prove a quadrilateral is a rhombus?
2. What are the properties of parallelograms?
3. How do you calculate the area of a rhombus?
4. What are the characteristics of a rectangle?
5. How do you find the perimeter of a triangle?

Tip: Understanding the properties and theorems related to different quadrilaterals can greatly help in solving geometry problems efficiently.