In parallelogram ABCD, line AC divides angle A in half. Find the angle at which the diagonals
| June 10, 2021 | education
In parallelogram ABCD, line AC divides angle A in half. Find the angle at which the diagonals of the parallelogram intersect.
The BCA angle is equal to the CAD angle since the secant AC intersects the parallel BC and AD, which means that these are cross-lying angles.
Since, according to the condition, the angle BAC is equal to the angle CAD, the angle BAC is equal to the angle BCA, and therefore the triangle ABC is isosceles, AB = BC.
In a parallelogram, opposite sides are equal, then CD = AB = AD = BC.
Since all sides of a parallelogram are equal, this parallelogram is a rhombus.
In a rhombus, the diagonals intersect at right angles.
Answer: The diagonals intersect at an angle of 90.
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