Do a two column proof.
Given: HI=FG
Prove: GH>FI
If FGI is a triangle,and GIH is a triangle, and they both share a common side, GI, and FIH is a straight line, how do you prove the answer?
gih line
To prove GH > FI using a two-column proof, you will need to provide a step-by-step logical argument, listing the statements and reasons. Here's how you can approach it:
Statement | Reason
---------|---------
1. HI = FG | Given
2. FG = HI | Symmetric property of equality
3. FGI is a triangle, GIH is a triangle | Given
4. FIH is a straight line | Given
5. FI + IG = FG | Triangle inequality theorem for FGI
6. GI + IH > IG | Triangle inequality theorem for GIH
7. GI + IH > FI | Substituting FG with HI (from statement 1)
8. GH > FI | Definition of greater than
By following these steps, you establish that GH is greater than FI based on the given information using the triangle inequality theorem and properties of equality.