I don't understand how to do this exactly can someone help?
List two sets of possible side lengths for two triangles. For example, you could list the side lengths 3, 4, and 5. One of your sets of side lengths should be able to form a triangle and one of your sets of side lengths should not be able to form a triangle.
Give the coordinates of three vertices that could be connected to form a right triangle on a coordinate plane. For example, the points left parenthesis negative 4 comma 2 right parenthesis, left parenthesis 4 comma 2 right parenthesis, left parenthesis 4 comma 6 right parenthesis and could be plotted and connected to form a right triangle.
To find two sets of possible side lengths for two triangles, you need to understand triangle inequality. The triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
For the first set, let's consider the side lengths 3, 4, and 5. Using the triangle inequality, we can check if this set of side lengths can form a triangle.
3 + 4 > 5 (True)
3 + 5 > 4 (True)
4 + 5 > 3 (True)
Since all three inequalities are true, the side lengths 3, 4, and 5 can form a triangle.
For the second set, let's consider the side lengths 1, 2, and 4. Using the triangle inequality, we can check if this set of side lengths can form a triangle.
1 + 2 > 4 (False)
1 + 4 > 2 (True)
2 + 4 > 1 (True)
Since one of the inequalities (1 + 2 > 4) is false, the side lengths 1, 2, and 4 cannot form a triangle.
Now, let's move on to the second question about finding three vertices for a right triangle on a coordinate plane. A right triangle has a 90-degree angle. One of the common scenarios for a right triangle on a coordinate plane is when one of the legs is on the x-axis, and the other leg is on the y-axis.
For example, you can use the three points (0, 0), (3, 0), and (0, 4) to create a right triangle. The point (0, 0) represents the origin, the point (3, 0) lies on the x-axis, and the point (0, 4) lies on the y-axis. If you plot these points and connect them, you will form a right triangle with a right angle at (0, 0).