Shape made by the bisectors of angles of a parallelogram is

Options

A. Rectangle
B. Square
C. Circle
D. Straight line

Answer

To determine the shape made by the angle bisectors of a parallelogram, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of a Parallelogram**:
A parallelogram has opposite angles that are equal and adjacent angles that are supplementary (sum to 180 degrees).

2. **Label the Angles**:
Let’s label the angles of the parallelogram as follows:
- Angle A = ∠A
- Angle B = ∠B
- Angle C = ∠C
- Angle D = ∠D
Here, ∠A + ∠B = 180° and ∠C + ∠D = 180°.

3. **Bisect the Angles**:
When we bisect each angle, we create two new angles for each original angle:
- ∠A is bisected into two angles: ∠1 and ∠2.
- ∠B is bisected into two angles: ∠3 and ∠4.
- ∠C is bisected into two angles: ∠5 and ∠6.
- ∠D is bisected into two angles: ∠7 and ∠8.

4. **Calculate the New Angles**:
Since ∠A + ∠B = 180°, we have:
- ∠1 + ∠2 = ∠A/2 + ∠B/2 = 90° (as ∠A and ∠B are supplementary).
Similarly, for the other pairs:
- ∠3 + ∠4 = 90°,
- ∠5 + ∠6 = 90°,
- ∠7 + ∠8 = 90°.

5. **Analyze the Triangles Formed**:
Each pair of bisected angles forms a triangle with the vertex at the intersection of the angle bisectors. For example, in triangle formed by angles ∠1, ∠2, and the vertex, the sum of the angles is:
- ∠1 + ∠2 + ∠3 = 180°.
Since ∠1 + ∠2 = 90°, we have ∠3 = 90°.

6. **Conclude the Shape**:
Since all the angles formed by the bisectors are 90°, the shape formed by the intersection of the angle bisectors of a parallelogram is a rectangle.

### Final Answer:
The shape made by the bisectors of the angles of a parallelogram is a **rectangle**.

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