A triangle can be formed when the sum of the lengths of any two sides is greater than the length of the third side.
Practice makes perfect
We want to determine whether we can draw a triangle with side lengths of 8 millimeters, 12 millimeters, and 13 millimeters. We can recall that a triangle can be formed when the sum of the lengths of any two sides is greater than the length of the third side. Let's compare the side lengths using a table!
Comparison
8mm+12mm? >13mm
8mm+13mm? >12mm
12mm+13mm? >8mm
20mm > 13mm âś“
21mm > 12mm âś“
25mm > 8mm âś“
Notice that each sum of the lengths of any two sides is greater than the length of the third side. This means that we can draw a triangle with the given side lengths. Now we can use a ruler and compass to draw our triangle. First we will draw a 13-millimeter side.
To find the position of the third vertex, we can open the compass to 12 millimeters. Then we can put the compass at one of the vertices and draw an arc.
Next, we will draw an arc with the compass open to 8 millimeters. Remember to put the compass at a different vertex than the previous side.
The point of intersection is the location of the third vertex of the triangle. Finally, we can draw our triangle. We can do so by connecting the vertices with the segments.
