# Task № 2.1

## Condition:

Masha was on vacation with her friends at the sea and drew a geometric figure in the sand.

Anya exclaimed: O, it's a triangle!

Rozalina objected: No, it's a quadrilateral!

Olya also spoke up: It's a square!

Alena did not stay out of it: It's a rectangle!

Only two of the four statements turned out to be true. What figures from the given list could Masha have drawn? Indicate all correct answers:

## Answer options:

○ Rhombus with a right angle

- Parallelogram with equal sides
- Rectangle with a perimeter of 166 cm
- Quadrilateral with sides of length 1, 5, 6, 10 cm


## Correct answer:

- Rectangle with a perimeter of 166 cm

Exact match of the answer - 1 point
# Solution.

If Olya was right, then Alyona and Rozalina would also be right, but in that case, there would already be at least three correct statements, which is impossible. Therefore, Olya is wrong. If Anya were right, then Rozalina, Olya, and Alyona would all be wrong, but then there would only be one correct statement, which is also impossible. Therefore, Anya is wrong. This means that Rozalina and Alyona must be right. In this case, the figure is a rectangle with unequal sides. Option 4 is not suitable, as it should have two pairs of equal sides. A parallelogram with equal sides is a rhombus, but a rhombus that is also a rectangle is a square, and we know that our figure is not a square, so option 2 is also not suitable. Option 1 is not suitable either, as a rhombus with a right angle is a square. Therefore, only option 3 remains. This is possible, for example, a rectangle with sides 1 and 82.