Question

Дан четырёхугольник ABCD, известно что АВ ||CD, BC ||AD. Докажите что биссекьрисы углов А и С параллельны или совпадают. помогите решить

Answer 1

Биссектриса угла С делит его на равные углы 1 и 2
Биссектриса угла А делит его на равные углы 3 и 4
Но раз АВ параллельно СD и ВС параллельно АD, то угол 2=углу 3 и 1=4 ,как накрест лежащие при двух параллельных прямых AB и CD секущей AC
Исходя из этого можно сказать,что угол А = углу С
А исходя из всего остального можно сказать,что биссектрисы этих углов совпадают.

Answer 2

Given Information:

We are given a quadrilateral ABCD, where AB is parallel to CD and BC is parallel to AD.

To Prove:

We need to prove that the bisectors of angles A and C are parallel or coincident.

Proof:

To prove that the bisectors of angles A and C are parallel or coincident, we can use the property that if two lines are parallel to the same line, then they are parallel to each other.

Let's consider the bisector of angle A. We can denote it as line l1.

Now, let's consider the bisector of angle C. We can denote it as line l2.

Since AB is parallel to CD and BC is parallel to AD, we can conclude that angles A and C are corresponding angles. Corresponding angles formed by parallel lines are congruent.

Therefore, angle A is congruent to angle C.

Since the bisectors of angles A and C divide their respective angles into two congruent angles, we can conclude that line l1 is parallel to line l2.

Hence, we have proved that the bisectors of angles A and C are parallel or coincident.

Conclusion:

We have proved that the bisectors of angles A and C in quadrilateral ABCD, where AB is parallel to CD and BC is parallel to AD, are parallel or coincident.

Note: The proof provided above is based on the given information and the properties of parallel lines and congruent angles.