The primary disadvantage of comparing line segments by mere observation is the potential for inaccuracies and subjective interpretation.

1. Inaccuracy: Human observation is prone to errors, and judgments about the equality or length of line segments might not always be precise. Without measurements or specific criteria, it's challenging to accurately determine whether two line segments are equal in length.

2. Subjectivity: Perception can vary from person to person. What one individual perceives as equal might appear different to another. Without objective measurements or standards, subjective judgments can lead to inconsistencies and disagreements.

3. Lack of Precision: Mere observation lacks precision compared to using mathematical tools or techniques. When dealing with geometric figures or mathematical problems, relying solely on observation can lead to imprecise results.

4. Limited Applicability: Observation-based comparisons might work for simple cases but become increasingly unreliable as geometric figures or line segments become more complex. In mathematical contexts or when precision is crucial, relying on observation alone is inadequate.

In summary, while observation can provide initial insights, it's essential to complement it with precise measurements, mathematical techniques, or tools to ensure accuracy and reliability, especially in mathematical or geometric contexts.

Using a divider rather than a ruler to measure the length of a line segment can offer several advantages:

1. Precision: Dividers typically have sharper points than rulers, allowing for more precise placement on the endpoints of the line segment. This precision helps ensure that the measurement accurately reflects the length of the segment.

2. Avoiding Parallax Errors: When using a ruler, there's a risk of parallax errors, where the position of the observer's eye affects the perceived position of the markings on the ruler. Dividers eliminate this issue because their points can be placed directly on the endpoints of the segment without needing to align with markings.

3. Consistency: Dividers provide consistent results regardless of the scale or markings on the ruler. With a ruler, variations in the thickness of the markings or the alignment of the observer's eye can lead to inconsistent measurements.

4. Versatility: Dividers can be adjusted to match the length of the segment precisely without the need for additional markings or measurements. This versatility makes dividers suitable for measuring segments of any length or scale.

5. Minimizing Damage: Dividers exert less pressure on the paper or surface being measured compared to rulers, reducing the risk of causing indentations or damage to delicate materials.

Overall, while rulers have their uses, dividers are often preferred for precise and consistent measurements of line segments due to their sharper points, avoidance of parallax errors, versatility, and gentler treatment of materials.

To determine which point lies between the other two, we can compare the sum of the lengths of two line segments with the length of the third segment.

Let's compare the sum of AB and BC with AC:

AB + BC = 5 cm + 3 cm = 8 cm

Since AB + BC = AC (8 cm), this means that points A and C are consecutive and point B lies between them.

So, point B lies between points A and C.

Sure, let's draw five triangles and measure their sides. Then, we'll check if the sum of the lengths of any two sides is always less than the third side. For simplicity, I'll denote the sides of each triangle as aa, bb, and cc.

1. Triangle 1: Let's say a=3a=3 cm, b=4b=4 cm, c=5c=5 cm (a Pythagorean triplet). Checking the triangle inequality: a+b>ca+b>c is true, a+c>ba+c>b is true, and b+c>ab+c>a is true. So, this triangle follows the triangle inequality.

2. Triangle 2: Let's say a=5a=5 cm, b=6b=6 cm, c=2c=2 cm. Checking the triangle inequality: a+b>ca+b>c is true, a+c>ba+c>b is true, and b+c>ab+c>a is false (5 + 2 is not greater than 6). So, this triangle does not follow the triangle inequality.

3. Triangle 3: Let's say a=7a=7 cm, b=2b=2 cm, c=9c=9 cm. Checking the triangle inequality: a+b>ca+b>c is true, a+c>ba+c>b is true, and b+c>ab+c>a is true. So, this triangle follows the triangle inequality.

4. Triangle 4: Let's say a=4a=4 cm, b=10b=10 cm, c=5c=5 cm. Checking the triangle inequality: a+b>ca+b>c is true, a+c>ba+c>b is false (4 + 5 is not greater than 10), and b+c>ab+c>a is true. So, this triangle does not follow the triangle inequality.

5. Triangle 5: Let's say a=8a=8 cm, b=2b=2 cm, c=4c=4 cm. Checking the triangle inequality: a+b>ca+b>c is true, a+c>ba+c>b is true, and b+c>ab+c>a is false (2 + 4 is not greater than 8). So, this triangle does not follow the triangle inequality.

Based on the measurements and checks, not all the triangles follow the triangle inequality theorem. Specifically, triangles 2, 4, and 5 violate the inequality.

To find the fraction of a clockwise revolution that the hour hand of a clock turns through when it goes from 3 to 9, we first need to determine the total angle turned by the hour hand in a clockwise direction.

The total angle of a clock is 360 degrees. The hour hand moves through 12 hours to complete one full revolution.

From 3 to 9, the hour hand moves through 6 hours.

So, the fraction of a clockwise revolution turned through by the hour hand from 3 to 9 is:

Fraction=Number of hours passed/Total hours in a clock=6/12=1/2

Therefore, the hour hand turns through 1221 of a clockwise revolution when it goes from 3 to 9 on a clock.