Question 19 of 22intermediate🔧 ApplyShort Answer3 marks

Mark any three points on your paper that are not on one line. Label them A, B, C. 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? Write them down, and mark each of them with a curve as in Fig. 2.9.

Correct Answer

Lines: Three lines can be drawn through pairs of three non-collinear points: Line AB Line BC Line CA ∴ 3 lines can be drawn.

Angles: Three angles can be named: ∠ABC (or ∠CBA) ∠BCA (or ∠ACB) ∠CAB (or ∠BAC) ∴ 3 angles can be named.

Each angle is formed at one of the three vertices where two lines meet.

Exercise: Figure it Out (Section 2) | Q: 5 | (Chapter: Page 8)
For More Understanding

Explanation

The chapter states that 'any two points determine a unique line.' With three non-collinear points A, B, C, we can form three lines: AB, BC, and CA. These three lines form a triangle with three vertices. At each vertex, an angle is formed by the two lines meeting there. The angles are ABC (at vertex B), BCA (at vertex C), and CAB (at vertex A). Each angle should be marked with a small curve at the vertex.

Solution Steps

  1. Mark three non-collinear points A, B, C on your paper.

  2. Draw line AB through points A and B.

  3. Draw line BC through points B and C.

  4. Draw line CA through points C and A.

  5. Count the total lines: 3 lines (AB, BC, CA).

  6. Name the angles: ∠ABC (or ∠CBA), ∠BCA (or ∠ACB), ∠CAB (or ∠BAC).

  7. Mark each angle with a curve at the vertex.

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