生成该题目的讲题视频,要求用画图的方式讲解呈现,讲解结构按照读题身体,思路启发,步骤讲解等顺序完成,要求时间控制在2分钟左右---**Question Stem:**
淘气有两根塑料小棒,如下图所示。(单位:厘米)
他想剪断其中一根,把剪后的三根小棒首尾相连围一个三角形。以下四种剪法中,可以围成三角形的是( )。
**Translation of Question Stem:**
Taoqi has two plastic sticks, as shown in the figure below. (Unit: cm)
He wants to cut one of them, and connect the three sticks end-to-end to form a triangle. Among the following four cutting methods, which one can form a triangle?
**Initial Diagram Description:**
* **Type:** Diagram illustrating two line segments (representing plastic sticks) with their lengths indicated.
* **Elements:**
* A top horizontal line segment, labeled "8". This represents a plastic stick of 8 cm length. It has 8 equal markings along its length.
* A bottom horizontal line segment, labeled "5". This represents a plastic stick of 5 cm length. It has 5 equal markings along its length.
* **Context:** These are the initial sticks available.
**Options:**
To determine which cutting method can form a triangle, we need to apply the Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
**Option A:**
* **Diagram Description:** Shows the 8 cm stick untouched. The 5 cm stick is shown with a pair of scissors indicating a cut at its midpoint (at the 2.5 cm mark).
* **Resulting Stick Lengths:**
* One stick: 8 cm
* Two sticks: 2.5 cm, 2.5 cm (from cutting the 5 cm stick in half)
* **Check Triangle Inequality:**
* 2.5 + 2.5 = 5. Is 5 > 8? No.
* **Conclusion:** Cannot form a triangle.
**Option B:**
* **Diagram Description:** Shows the 8 cm stick untouched. The 5 cm stick is shown with a pair of scissors indicating a cut approximately 1 cm from its left end.
* **Resulting Stick Lengths:**
* One stick: 8 cm
* Two sticks: 1 cm, 4 cm (from cutting the 5 cm stick into pieces of 1 cm and 4 cm)
* **Check Triangle Inequality:**
* 1 + 4 = 5. Is 5 > 8? No.
* **Conclusion:** Cannot form a triangle.
**Option C:**
* **Diagram Description:** Shows the 5 cm stick untouched. The 8 cm stick is shown with a pair of scissors indicating a cut at its midpoint (at the 4 cm mark).
* **Resulting Stick Lengths:**
* One stick: 5 cm
* Two sticks: 4 cm, 4 cm (from cutting the 8 cm stick in half)
* **Check Triangle Inequality:**
* 4 + 4 = 8. Is 8 > 5? Yes.
* 4 + 5 = 9. Is 9 > 4? Yes.
* **Conclusion:** Can form a triangle. (This option satisfies the triangle inequality for all combinations of sides).
**Option D:**
* **Diagram Description:** Shows the 5 cm stick untouched. The 8 cm stick is shown with a pair of scissors indicating a cut approximately 1 cm from its right end (or 7 cm from its left end).
* **Resulting Stick Lengths:**
* One stick: 5 cm
* Two sticks: 7 cm, 1 cm (from cutting the 8 cm stick into pieces of 7 cm and 1 cm)
* **Check Triangle Inequality:**
* 1 + 5 = 6. Is 6 > 7? No.
* **Conclusion:** Cannot form a triangle.