less than a right greater than a right Jeff has a square piece of art paper. He cuts across it from one corner to the opposite corner to make two pieces. What is the total number of sides and angles in both of the new shapes
The Correct Answer and Explanation is:
Correct Answer: 6 sides and 6 angles
Explanation
Jeff starts with a square piece of art paper. A square has 4 sides and 4 angles, all equal in length and all right angles (each measuring 90°).
When Jeff cuts across the square from one corner to the opposite corner, he is making a diagonal cut. This kind of cut divides the square into two right-angled triangles.
Let’s analyze what happens after the cut:
- A diagonal connects two opposite corners of the square.
- The diagonal becomes one side of each of the two resulting shapes.
- Since a square has two diagonals and each diagonal cuts it exactly in half, the two resulting shapes are congruent right-angled triangles.
Each triangle:
- Has 3 sides: one being half the square’s diagonal (the hypotenuse) and the other two being sides of the original square.
- Has 3 angles: one right angle (90°) from the original square, and two acute angles.
So, for each triangle, we have:
- 3 sides
- 3 angles
Since there are two triangles, we multiply:
- 3 sides×2=6 sides3 \text{ sides} \times 2 = 6 \text{ sides}
- 3 angles×2=6 angles3 \text{ angles} \times 2 = 6 \text{ angles}
Thus, after the cut, the total number of sides is 6, and the total number of angles is 6.
Important Clarification:
Some might think the answer should still be 4 sides and 4 angles, since the shape is still composed of the original parts. However, once the square is cut into two separate triangles, each triangle becomes an individual polygon with 3 sides and 3 angles. Together, they make 6 sides and 6 angles in total.
So, the correct final answer is:
✅ 6 sides and 6 angles.
