Answer: ≥ without the line on the bottom.
Step-by-step explanation:
I am assuming the expression you are talking about are
and
.
If we were to replace w with 4 and calculate, we will find the answer:
Since the first expression, , is bigger than the second expression, the correct symbol to use is ≥ without the line on the bottom.
====================================================
Explanation:
A drawing may be helpful to see what's going on. Check out the diagram below. This is one way of drawing out the two triangles. The locations of the points don't really matter, and neither does the the orientation of how you rotate things. What does matter is we have the right points connected to form the segments mentioned.
----------
For now, focus on triangle TIP only. In order to have this be isosceles, we must make TP = 5 or TP = 7.
If TP = 5, then it's the same length as TI.
If TP = 7, then it's the same length as PI.
In either case, we have exactly two sides the same length (the other side different) which is what it means for a triangle to be isosceles.
----------
Let's consider triangle TOP. For it to be isosceles, we must have two sides the same length. We already locked in TP to be either 5 or 7 in the previous section above. So there's no way that TP could be 11 units long to match up with PO = 11.
If TP = 5, then OT must also be 5 units long so that triangle TOP is isosceles.
If TP = 7, then OT = 7 for similar reasoning.
Either way, TP only has two choices on what it could be.
----------
In short, we basically just write the first two values given to us to get the two triangles to be isosceles. We can't use TP = 11 as it would make triangle TIP to be scalene (all sides are different lengths).
