If <ABD and <DBC form a linear pair at vertex B, which three points, A, B, C, or D, are collinear?

When two angles form a linear pair, they are adjacent to each other and their non-common sides form a straight line. 

Given that \(\angle ABD\) and \(\angle DBC\) form a linear pair at vertex \(B\), this means that points \(A\), \(B\), and \(C\) are collinear. This is because the line passing through \(A\), \(B\), and \(C\) forms a straight line with the angles \(\angle ABD\) and \(\angle DBC\) being adjacent.

So, the three collinear points are **A, B, and C**.

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Here are some related questions:
1. What is the definition of a linear pair of angles?
2. How can you prove that three points are collinear using a linear pair?
3. What is the relationship between supplementary angles and linear pairs?
4. Can two obtuse angles form a linear pair? Why or why not?
5. How does the concept of a linear pair relate to parallel lines?

**Tip:** Understanding linear pairs is essential because they often help in solving problems involving angles and lines

Explore how angles form linear pairs and understand collinearity in geometry. Learn about the relationship between angles ABD and DBC at vertex B and determine collinearity of points A, B, and C. Suitable for students in Grades 7-9.

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