Prove Segment Equality: Is BC Equal to CB in Triangle Construction?

Segment Notation with Direction Independence

According to figure BC=CB?

AAABBBCCCDDDEEE

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine whether BC is equal to CB
00:03 The side is always the same side, therefore they are equal
00:12 It doesn't matter which letter is written first, it's the same side
00:17 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

According to figure BC=CB?

AAABBBCCCDDDEEE

2

Step-by-step solution

In geometry, the distance or length of a line segment between two points is the same, regardless of the direction in which it is measured. Consequently, the segments denoted by BC BC and CB CB refer to the same segment, both indicating the distance between points B and C.

Hence, the statement "BC = CB" is indeed True.

3

Final Answer

True

Key Points to Remember

Essential concepts to master this topic
  • Rule: Line segment length is independent of measurement direction
  • Technique: BC and CB both represent distance between points B and C
  • Check: Distance from B to C equals distance from C to B ✓

Common Mistakes

Avoid these frequent errors
  • Thinking BC and CB are different measurements
    Don't treat BC and CB as different values = confusion about segment notation! This misconception comes from confusing segments with vectors. Always remember that line segment length is the same regardless of which endpoint you start from.

Practice Quiz

Test your knowledge with interactive questions

Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

Are BC and CB really the same thing?

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Yes! BC and CB represent the same line segment. Think of it like measuring the distance between two cities - it's the same whether you drive from City B to City C or from City C to City B.

When would BC not equal CB?

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In vector mathematics, BC and CB would be opposite vectors. But for line segments (measuring distance), they're always equal. This question is about segments, not vectors.

How can I remember this rule?

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Think of a ruler! If you measure from the 2-inch mark to the 5-inch mark, you get 3 inches. If you measure from the 5-inch mark to the 2-inch mark, you still get 3 inches of distance.

What's the difference between a segment and a line?

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A line segment has two endpoints and a measurable length. A line extends infinitely in both directions. The notation BC BC refers to the segment between points B and C.

Do I need to worry about the order of letters?

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For distance measurements, no! BC = CB always. However, in more advanced topics like vectors or directed line segments, order can matter. For basic geometry, focus on distance being the same.

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