IN PARALLELOGRAM ABCD, ANGLE BISECTOR OF ANGLE A BISECTS BC. WILL ANGLE BISECTOR OF ANGLE B ALSO BISECT AD?
If you call it an angle bisector, then it will bisect.
To determine whether the angle bisector of angle B in parallelogram ABCD also bisects AD, we can use the properties of parallelograms and angle bisectors.
In a parallelogram, opposite angles are congruent. Therefore, we have:
∠A ≅ ∠C
∠B ≅ ∠D
Now, let's consider the angle bisector of angle A, which bisects side BC. This means that it divides angle A into two congruent angles:
∠BAE ≅ ∠EAC
Since ∠A ≅ ∠C, let's name these congruent angles as follows:
∠BAE = ∠EAC = x
Now, let's consider the angle bisector of angle B. If it bisects side AD, it should divide angle B into two congruent angles as well:
∠EBF ≅ ∠FBD
Since ∠B ≅ ∠D, let's name these congruent angles as follows:
∠EBF = ∠FBD = y
To determine whether ∠EBF and ∠FBD are congruent, we need to compare them to the congruent angles we found earlier.
From the given information, we know that ∠BAE ≅ ∠EAC = x. Since ∠BAE and ∠EBF share the side BE, we can confidently say that ∠BAE = ∠EBF = x.
However, there is no guarantee that ∠EAC and ∠FBD are congruent. Therefore, we cannot conclude that the angle bisector of angle B also bisects the side AD in parallelogram ABCD.