Identify the subject and grade level. Then, based on the OCR, identify the task. Finally, answer question 1 and question 2.

Subject and Grade Level:

Subject: Mathematics

Grade Level: Unknown (likely middle school, given the topic)

Task Identification:

The task is a geometry review worksheet focusing on angles, triangles, and parallelograms. Specifically, it asks to select correct statements.

Answer to Question 1:

Question 1: Choose the correct statements (circle their numbers):

1) There exists a triangle with sides 5 cm, 6 cm, and 4 cm.

To determine if a triangle can exist with these side lengths, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

• 5 + 6 > 4 (11 > 4) - True
• 5 + 4 > 6 (9 > 6) - True
• 6 + 4 > 5 (10 > 5) - True

Since all conditions of the triangle inequality theorem are met, a triangle with sides 5 cm, 6 cm, and 4 cm can exist.

Answer for statement 1: True

Answer to Question 2:

2) A parallelogram can have angles of 25° and 165°.

In a parallelogram, consecutive angles are supplementary (add up to 180°), and opposite angles are equal.

If one angle is 25°, the consecutive angle must be 180° - 25° = 155°.

If one angle is 165°, the consecutive angle must be 180° - 165° = 15°.

The given angles are 25° and 165°. If these were two angles in the parallelogram, they would have to be either consecutive or opposite.

• If they were opposite, they would be equal, which they are not (25° ≠ 165°).
• If they were consecutive, their sum would be 180°. 25° + 165° = 190°, which is not 180°.

Therefore, a parallelogram cannot have angles of 25° and 165° simultaneously.

Answer for statement 2: False