in a parallelogram, the bisectors of any two consecutive angles intersect at right angle. AR and DC respectively and AL-CN
Note: A property of that parallelogram says that if a parallelogram has all sides equal, then their diagonal bisector intersects perpendicularly. An angle bisector is a ray that splits an angle into two consecutive congruent, smaller angles.
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The Bisectors of any Two Consecutive Angles of a Parallelogram Intersect at Right Angle
Concept Explanation
The Bisectors of Any Two Consecutive Angles Intersect at Right Angle: We know that parallelogram is a quadrilateral in which both the opposite pair of sides are parallel and equal to each other, The bisectors of any two consecutive angles intersect at right angle. | |
Theorem 5: In a parallelogram, the bisectors of any two consecutive angles intersect at right angle. GIVEN A parallelogram ABCD such that the bisectors of consecutive angles A and B intersect at P. To prove <APB = 90 Proof Since ABCD is a parallelogram. Therefore, AD Now, AD BC and transversal AB intersects them. ...(i) [ AO and BO are bisectors of <A and <B] In <1 + <APB + <2 = 180 90 + <APB = 180 [ From (i), <1 + <2 = 90] <APB = 90 | |
ILLUSTRATION: In the given figure, AP and BP are the bisectors of | |
Solution: In a parallelogram the angle bisectors of a parallelogram meet at right angles. As ABCD is a parallelogram. Therefore, AD BC Now, AD BC and transversal CD intersects them. [ Sum of consecutive interior angles is 180] [From Eq. 1] Hence Proved |
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