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If two parallel lines are intersected by a transversal then the bisectors of the interior angles form a :
- a)rhombus
- b)parallogram
- c)Square
- d)Rectangle
Correct answer is option 'D'. Can you explain this answer?
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If two parallel lines are intersected by a transversal then the bisect...
if two parallel lines are intersected by a transversal then prove that bisectors of the interior angles form a triangle.if two parallel lines are intersected by a transversal then prove that bisectors of the interior angles form a rectangle.
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If two parallel lines are intersected by a transversal then the bisect...
Explanation:
When two parallel lines are intersected by a transversal, eight angles are formed. These angles can be classified into two types:
1. Corresponding angles: Angles that are in the same position in relation to the transversal and the parallel lines.
2. Interior angles: Angles that are inside the parallel lines and on the same side of the transversal.
The bisectors of the interior angles will divide them into two equal parts. This means that each of the four interior angles will be divided into two equal angles.
The bisectors will also intersect each other at right angles. This is because the interior angles of a parallelogram are supplementary, and the bisectors divide each angle into two equal parts.
Why is it a rectangle?
A rectangle is a quadrilateral with four right angles. Since the bisectors of the interior angles of a parallelogram intersect at right angles, the resulting figure is a rectangle.
The opposite sides of a rectangle are parallel, and the adjacent sides are perpendicular. This property is satisfied by the figure formed when the bisectors of the interior angles of a parallelogram intersect.
Therefore, the correct answer to the question is option D, which states that the bisectors of the interior angles form a rectangle.
When two parallel lines are intersected by a transversal, eight angles are formed. These angles can be classified into two types:
1. Corresponding angles: Angles that are in the same position in relation to the transversal and the parallel lines.
2. Interior angles: Angles that are inside the parallel lines and on the same side of the transversal.
The bisectors of the interior angles will divide them into two equal parts. This means that each of the four interior angles will be divided into two equal angles.
The bisectors will also intersect each other at right angles. This is because the interior angles of a parallelogram are supplementary, and the bisectors divide each angle into two equal parts.
Why is it a rectangle?
A rectangle is a quadrilateral with four right angles. Since the bisectors of the interior angles of a parallelogram intersect at right angles, the resulting figure is a rectangle.
The opposite sides of a rectangle are parallel, and the adjacent sides are perpendicular. This property is satisfied by the figure formed when the bisectors of the interior angles of a parallelogram intersect.
Therefore, the correct answer to the question is option D, which states that the bisectors of the interior angles form a rectangle.
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If two parallel lines are intersected by a transversal then the bisectors of the interior angles form a :a)rhombusb)parallogramc)Squared)RectangleCorrect answer is option 'D'. Can you explain this answer?
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