Question

1. matching.

1.
35 mm
2.
17 mm
3.
20 mm
to form a triangle, the sum of the lengths of any two line segments must be
than the length of the third side.
the set of line segments
meet the requirements to form a triangle.

Explanation:

Step1: Recall Triangle Inequality

The triangle inequality theorem states that for three lengths \(a\), \(b\), \(c\) to form a triangle, \(a + b>c\), \(a + c>b\), and \(b + c>a\). In short, the sum of any two sides must be greater than the third side.

Step2: Check the Given Segments

The segments are \(17\) mm, \(20\) mm, and \(35\) mm.

• Check \(17 + 20\) vs \(35\): \(17+20 = 37\), and \(37>35\).
• Check \(17 + 35\) vs \(20\): \(17 + 35=52\), and \(52>20\).
• Check \(20 + 35\) vs \(17\): \(20 + 35 = 55\), and \(55>17\).

So the sum of any two line segments must be greater than the length of the third side, and the set \(17\) mm, \(20\) mm, \(35\) mm (all three) meet the requirements.

Answer:

First blank: greater
Second blank: (1, 2, 3) or "17 mm, 20 mm, 35 mm" (depending on the options, but based on the segments given, the three segments together satisfy the triangle inequality)