# Determining Lines and Angles from Four Non-Collinear Points

**URL:** <https://sorumatik.co/t/determining-lines-and-angles-from-four-non-collinear-points/667136>\
**Category:** Maths Question\
**Created:** [Haziran 28, 2026, 2:25ös UTC](https://sorumatik.co/t/determining-lines-and-angles-from-four-non-collinear-points/667136 "2026-06-28T14:25:58Z")\
**Posts on this page:** 4\
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**Author:** ![Qr48ywz6q2](https://sorumatik.co/letter_avatar_proxy/v4/letter/q/71e660/32.png) [@Qr48ywz6q2](https://sorumatik.co/u/Qr48ywz6q2)\
**Post date:** [Haziran 28, 2026, 2:25ös UTC](https://sorumatik.co/t/determining-lines-and-angles-from-four-non-collinear-points/667136/1 "2026-06-28T14:25:58Z")

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Lines and Angles  
Now mark any four points on your paper so that no three of them  
are on one line. Label them A, B, C, D. Draw all possible lines going  
through pairs of these points. How many lines do you get? Name  
them. How many angles can you name using A, B, C, D? Write them  
all down, and mark each of them with a curve as in Fig. 2.9.

 ![Soru Görseli](https://sorumatik.co/uploads/default/original/3X/1/d/1da3ff5c81d03557f7737d4727eda50d17470c2c.jpeg)

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**Author:** ![Egitim\_Danismani](https://sorumatik.co/user_avatar/sorumatik.co/egitim_danismani/32/86791_2.png) [@Egitim\_Danismani](https://sorumatik.co/u/Egitim_Danismani)\
**Post date:** [Haziran 28, 2026, 2:26ös UTC](https://sorumatik.co/t/determining-lines-and-angles-from-four-non-collinear-points/667136/2 "2026-06-28T14:26:04Z")

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## Determining Lines and Angles from Four Non-Collinear Points

💡 **RULE / FORMULA USED:**  
To find the number of unique lines passing through n points where no three points are collinear, we use the combination formula:

\text{Number of Lines} = \binom{n}{2} = \frac{n(n-1)}{2}

🧠 **SOLUTION STEPS:**

**Step 1 — Determine the Number of Lines**  
With n = 4 points (A, B, C, and D), we calculate the number of unique pairs:

\text{Lines} = \frac{4 \times (4-1)}{2} = \frac{12}{2} = 6

**Step 2 — Name the Unique Lines**  
By connecting every point to every other point, we get the following lines:

1. Line **AB**
2. Line **AC**
3. Line **AD**
4. Line **BC**
5. Line **BD**
6. Line **CD**

**Step 3 — Identify the Possible Angles**  
When you draw these 6 lines, you form a quadrilateral (ABCD) with two diagonals (AC and BD). At each of the 4 points, 3 lines intersect, creating 3 distinct angles at each vertex.

- **At vertex A:** \angle BAC, \angle CAD, \angle BAD
- **At vertex B:** \angle ABC, \angle ABD, \angle CBD
- **At vertex C:** \angle BCA, \angle ACD, \angle BCD
- **At vertex D:** \angle ADB, \angle BDC, \angle ADC

━━━━━━━━━━━━━━━━━━━━━━━━━━━  
✅ **ANSWER:**  
**Total Lines:** 6 (AB, AC, AD, BC, BD, CD)  
**Total Angles:** 12 (Listed above)  
━━━━━━━━━━━━━━━━━━━━━━━━━━━

🎯 **[KEY CONCEPTS:]**

**1. Non-collinear Points**

- **[Definition:]** Points that do not lie on the same straight line.
- **[In this problem:]** Because “no three points are on one line,” every pair of points forms a unique new line without overlapping.

**2. Vertex**

- **[Definition:]** The common endpoint where two or more rays or line segments meet.
- **[In this problem:]** Points A, B, C, and D act as vertices where multiple angles are formed.

⚠ **[COMMON MISTAKES:]**

**❌ Overcounting Lines**

- **[Wrong:]** Listing Line AB and Line BA as two different lines.
- **[Right:]** Recognizing that Line AB and BA are the same spatial object.
- **[Why it’s wrong:]** In geometry, a line passing through two points is unique regardless of the order of the points named.

**❌ Missing Interior Angles**

- **[Wrong:]** Only naming the four corners of the outer shape (like \angle ABC).
- **[Right:]** Including the angles created by the diagonals (like \angle ABD and \angle CBD).
- **[Why it’s wrong:]** Every pair of lines meeting at a point creates a measurable angle that must be accounted for.

Would you like me to explain how the number of lines would change if three of the points were actually on the same line?

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**Author:** ![Qr48ywz6q2](https://sorumatik.co/letter_avatar_proxy/v4/letter/q/71e660/32.png) [@Qr48ywz6q2](https://sorumatik.co/u/Qr48ywz6q2)\
**Post date:** [Haziran 28, 2026, 2:28ös UTC](https://sorumatik.co/t/determining-lines-and-angles-from-four-non-collinear-points/667136/3 "2026-06-28T14:28:17Z")

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draw an angle

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**Author:** ![Egitim\_Danismani](https://sorumatik.co/user_avatar/sorumatik.co/egitim_danismani/32/86791_2.png) [@Egitim\_Danismani](https://sorumatik.co/u/Egitim_Danismani)\
**Post date:** [Haziran 28, 2026, 2:28ös UTC](https://sorumatik.co/t/determining-lines-and-angles-from-four-non-collinear-points/667136/4 "2026-06-28T14:28:24Z")

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## How to Draw and Name an Angle

💡 **[RULE / FORMULA USED:]**  
An **angle** is formed by two rays (called sides) that share a common endpoint (called the **vertex** ). It is usually named using three letters, with the vertex letter always in the middle.

🧠 **[SOLUTION STEPS:]**

**Step 1 — Mark the Vertex**  
Pick a point on your paper and label it. Let’s call this point **B**. This will be the “corner” of your angle.

**Step 2 — Draw the First Ray**  
Using a ruler, draw a straight line starting from point **B** extending in any direction. Mark another point on this line and label it **A**. This is ray BA.

**Step 3 — Draw the Second Ray**  
Starting again from the same vertex **B** , draw another straight line in a different direction. Mark a point on this line and label it **C**. This is ray BC.

**Step 4 — Mark the Angle**  
Draw a small curved arc near point **B** , connecting the inside of the two rays. This curve represents the rotation or opening between the sides.

━━━━━━━━━━━━━━━━━━━━━━━━━━━  
✅ **[ANSWER:]**  
You have now drawn **Angle ABC** (written as \angle ABC or \angle CBA).

- **Vertex:** Point B
- **Sides:** Ray BA and Ray BC  
━━━━━━━━━━━━━━━━━━━━━━━━━━━

🎯 **[KEY CONCEPTS:]**

**1. Vertex**

- **[Definition:]** The point where the two rays meet.
- **[In this problem:]** Point **B** is the vertex.

**2. Interior of an Angle**

- **[Definition:]** The area “inside” the two rays where you draw the curve.
- **[In this problem:]** The curve indicates we are measuring the space between BA and BC.

⚠ **[COMMON MISTAKES:]**

**❌ Incorrect Naming Order**

- **[Wrong:]** Naming the angle \angle BAC if the vertex is at B.
- **[Right:]** Naming it \angle ABC or \angle B.
- **[Why it’s wrong:]** The middle letter must always be the vertex.

**❌ Drawing Curved Sides**

- **[Wrong:]** Drawing wavy or freehand lines for the sides.
- **[Right:]** Using a straightedge or ruler.
- **[Why it’s wrong:]** In geometry, the sides of an angle are parts of straight lines (rays).

Would you like to learn how to use a protractor to draw an angle with a specific measurement, such as 45^\circ or 90^\circ?