If a transversal line cuts two parallel lines then bisector of internal angle formed a

Options

A. rectangle
B. square
C. rhombus
D. parallelogram

Answer

To solve the question, "If a transversal line cuts two parallel lines, then the bisector of the internal angle formed will create what type of figure?" we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Parallel Lines and Transversal**:
- Let’s denote the two parallel lines as line A and line B.
- The transversal line that cuts across these two parallel lines can be denoted as line PQ.

2. **Label the Points of Intersection**:
- Let the point where line PQ intersects line A be point R and where it intersects line B be point S.

3. **Identify the Internal Angles**:
- The angles formed at point R (between line A and line PQ) are internal angles. Let’s label these angles as angle 1 and angle 2.
- Similarly, at point S, we have angle 3 and angle 4.

4. **Draw the Angle Bisectors**:
- The bisector of angle 1 will create a line segment from point R, and the bisector of angle 2 will also create a line segment from point R.
- The same applies to angles 3 and 4 at point S.

5. **Label the Bisectors**:
- Let the bisector of angle 1 be line RE and the bisector of angle 2 be line RF.
- Similarly, let the bisector of angle 3 be line SE and the bisector of angle 4 be line SF.

6. **Analyze the Angles**:
- Since angle 1 and angle 2 are equal (as they are bisected), we can say that angle 1 + angle 2 = 180° (straight line).
- Therefore, if angle 1 = angle 2, we can express this as 2 * angle 2 = 180°, leading to angle 2 = 90°.

7. **Repeat for Angles at Point S**:
- Similarly, for angles at point S, angle 3 + angle 4 = 180°.
- Since angle 3 = angle 4, we can express this as 2 * angle 4 = 180°, leading to angle 4 = 90°.

8. **Conclusion About the Figure**:
- Since we have established that the angles formed by the bisectors at points R and S are both 90°, we can conclude that the figure formed by lines RE, RF, SE, and SF is a quadrilateral with all angles being 90°.

9. **Determine the Type of Quadrilateral**:
- A quadrilateral with all angles equal to 90° is classified as a rectangle.
- Since we have two pairs of opposite sides that are equal (due to the properties of parallel lines and angle bisectors), we can conclude that this figure is a rectangle.

### Final Answer:
The bisectors of the internal angles formed when a transversal cuts two parallel lines create a rectangle.