Question

Учитель начертил на классной доске четырехугольник. Янош утверждал, что это квадрат. Имре считал, что четырехугольник - трапеция. Мария думала, что на доске изображен ромб. Ева назвала четырехугольник параллелограммом. Выслушав каждого и внимательно изучив свойства четырехугольника, учитель установил, что ровно 3 из 4 суждений истинны и ровно 1 суждение ложно.Какой четырехугольник начертил учитель на классной доске?Дополнительный вопрос:где почесать собаку,чтобы та подергала ногой? В учебнике все списала!!!

Answer 1

Учитель начертил , конечно же, квадрат, тогда истинными будут утверждения о
1) квадрате
2) ромбе, т.к. ромб- - это четырехугольник с равными сторонами, тоесть квадрат является и ромбом;
3) параллелограмме, т. к. параллелограмм- это четырёхугольник с равными противоположными сторонами и углами, т.е. квадрат является и параллелограммом.
Ложно утверждение о трапеции.

Answer 2

The Shape on the Classroom Board

The teacher drew a quadrilateral on the classroom board, and four students, Yanosh, Imre, Maria, and Eva, each had different opinions about the shape. Yanosh claimed it was a square, Imre believed it was a trapezoid, Maria thought it was a rhombus, and Eva called it a parallelogram. The teacher carefully examined the properties of the quadrilateral and determined that exactly 3 out of the 4 statements were true, while 1 statement was false. The question is, what type of quadrilateral did the teacher draw on the classroom board?

To solve this problem, let's analyze the statements made by each student and determine which ones are true and which one is false.

- Yanosh claimed it was a square. - Imre believed it was a trapezoid. - Maria thought it was a rhombus. - Eva called it a parallelogram.

Based on the information given, we know that exactly 3 out of these 4 statements are true. Let's evaluate each statement:

1. Yanosh claimed it was a square. - If Yanosh's statement is true, then the quadrilateral must be a square. - If Yanosh's statement is false, then the quadrilateral is not a square.

2. Imre believed it was a trapezoid. - If Imre's statement is true, then the quadrilateral must be a trapezoid. - If Imre's statement is false, then the quadrilateral is not a trapezoid.

3. Maria thought it was a rhombus. - If Maria's statement is true, then the quadrilateral must be a rhombus. - If Maria's statement is false, then the quadrilateral is not a rhombus.

4. Eva called it a parallelogram. - If Eva's statement is true, then the quadrilateral must be a parallelogram. - If Eva's statement is false, then the quadrilateral is not a parallelogram.

Since exactly 3 out of the 4 statements are true, we can conclude that the false statement is the one made by Maria, who thought it was a rhombus. Therefore, the quadrilateral drawn by the teacher on the classroom board is not a rhombus.

To determine the exact type of quadrilateral, we need more information or properties of the shape. Without additional details, it is not possible to determine whether the quadrilateral is a square, trapezoid, or parallelogram.