Naming Rays and Identifying the Starting Point in Fig. 2.5

Maths Question
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Fig. 2.4
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the rays shown in Fig. 2.5. Is T the starting po\int of eachan

these rays?
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Fig. 2.5

Soru Görseli
Soru Görseli1024×550 95.5 KB

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Naming Rays and Identifying the Starting Point in Fig. 2.5

:light_bulb: [RULE / FORMULA USED:]
A ray is a part of a line that has one fixed starting point (called the initial point or origin) and extends infinitely in one direction. When naming a ray, the first letter must be the starting point, and the second letter is any other point on the ray (e.g., \vec{TA}).

:brain: [SOLUTION STEPS:]

Step 1 — Identify the Rays in the Figure
By looking at Fig. 2.5, we see lines starting from point T and passing through other points. An arrow indicates the direction of infinite extension.

  • The first ray starts at T and passes through A. This is ray \vec{TA}.
  • The second ray starts at T and passes through N and B. This can be named ray \vec{TN} or ray \vec{TB} (they represent the same ray).

Step 2 — Determine the Starting Point
Observe the point where the lines originate without an arrow. Both lines originate from the vertex labeled T.

  • For ray \vec{TA}, the starting point is T.
  • For ray \vec{TN} (or \vec{TB}), the starting point is T.

Step 3 — Conclusion
Since both rays originate from the same vertex T before extending towards their respective directions, T is indeed the starting point for each.

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:white_check_mark: [ANSWER:]

  1. The rays shown are Ray \vec{TA} and Ray \vec{TB} (or \vec{TN}).
  2. Yes, T is the starting point of each of these rays.
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:bullseye: [KEY CONCEPTS:]

1. Ray

  • [Definition:] A geometric figure with one endpoint that extends forever in one direction.
  • [In this problem:] We identified two rays (\vec{TA}, \vec{TB}) sharing a common endpoint.

2. Starting Point (Initial Point)

  • [Definition:] The point where a ray begins.
  • [In this problem:] Point T serves as the origin for both rays forming the angle.

:warning: [COMMON MISTAKES:]

:cross_mark: Naming the ray in reverse

  • [Wrong:] Naming the ray as \vec{AT} or \vec{BT}.
  • [Right:] \vec{TA} and \vec{TB}.
  • [Why it’s wrong:] In geometry, the first letter of a ray must be its starting point. \vec{AT} would mean the ray starts at A and goes toward T, which is the opposite of the figure.

Would you like me to explain the difference between a ray, a line segment, and a line using this figure?