Question

1. Які з тверджень вiрнi? 1) Якщо у чотирикутнику два кути рівні, то вiн е паралелограмом2) Якщо у чотирикутнику протилежні сторони рівні, то він є паралелограмом 3)Якщо у чотирикутнику одна з діагоналей точкою перетину ділиться пополам, то він є паралелограмом 4)Якщо у чотирикутнику протилежні кути рівні, то він є паралелограмом 5)Якщо у чотирикутнику два протилежні кути рівні, то він є паралелограмом​

Answer 1

Вірні: 2, 3, 4



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Answer 2

Statements about Parallelograms

1) If a quadrilateral has two equal angles, then it is a parallelogram. 2) If a quadrilateral has opposite sides that are equal, then it is a parallelogram. 3) If a quadrilateral's diagonal bisects at the point of intersection, then it is a parallelogram. 4) If a quadrilateral has opposite angles that are equal, then it is a parallelogram. 5) If a quadrilateral has two opposite angles that are equal, then it is a parallelogram.

Let's verify each statement:

1) If a quadrilateral has two equal angles, then it is a parallelogram. - This statement is incorrect. A quadrilateral with two equal angles is not necessarily a parallelogram. For example, a trapezoid can have two equal angles but is not a parallelogram.

2) If a quadrilateral has opposite sides that are equal, then it is a parallelogram. - This statement is correct. A quadrilateral with opposite sides that are equal is a parallelogram. This property is known as the opposite sides of a parallelogram are congruent.

3) If a quadrilateral's diagonal bisects at the point of intersection, then it is a parallelogram. - This statement is incorrect. A quadrilateral with a diagonal that bisects at the point of intersection is not necessarily a parallelogram. For example, a kite has a diagonal that bisects at the point of intersection but is not a parallelogram.

4) If a quadrilateral has opposite angles that are equal, then it is a parallelogram. - This statement is incorrect. A quadrilateral with opposite angles that are equal is not necessarily a parallelogram. For example, a rectangle has opposite angles that are equal but is not a parallelogram.

5) If a quadrilateral has two opposite angles that are equal, then it is a parallelogram. - This statement is correct. A quadrilateral with two opposite angles that are equal is a parallelogram. This property is known as the opposite angles of a parallelogram are congruent.

In summary, statements 2 and 5 are correct, while statements 1, 3, and 4 are incorrect.