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Choose the appropriate term for <BAD and <CAD if AD is an angle bisector

In the diagram you uploaded, it appears that \( \overrightarrow{AD} \) is an angle bisector of \( \angle BAC \). This means that:

1. \( \angle BAD \) is equal to \( \angle CAD \), since an angle bisector divides an angle into two equal parts.

Therefore, we can conclude:
- \( \angle BAD \) and \( \angle CAD \) are **congruent angles**.

Would you like any further clarification on this concept? 

Here are some related questions to consider:

1. What is the relationship between the lengths of segments \( AB \) and \( AC \) if \( \overrightarrow{AD} \) bisects \( \angle BAC \)?
2. How can the angle bisector theorem be applied to this situation?
3. Can you calculate the measure of \( \angle BAD \) if the full \( \angle BAC \) is known?
4. How would the diagram change if \( \overrightarrow{AD} \) were not an angle bisector?
5. What are the implications of \( \overrightarrow{AD} \) being a median or altitude instead of an angle bisector?

**Tip:** In geometry, an angle bisector not only divides an angle into two equal parts, but it also has interesting properties related to the lengths of opposite sides in a triangle (angle bisector theorem).

Choose the appropriate term for ∠BAD and ∠CAD if AD is an angle bisector

Learn how to identify congruent angles when given an angle bisector, with an example of AD bisecting ∠BAC into ∠BAD and ∠CAD. This problem highlights key concepts of geometry and the Angle Bisector Theorem, suitable for students in Grades 8-10.

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