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Proof Tables
- Thread starter pixa241
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HallsofIvy
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- Jan 27, 2012
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Look at the two triangles EHI and IFG. How many "parts" of those two triangles are congruent?
Look at the two triangles EHI and IFG. How many "parts" of those two triangles are congruent?
From what I see 3 parts of the two triangles are congruent. Angle EHI is congruent to Angle FGI. Angle EIH is congruent to Angle FIG. Angle HEI is congruent to Angle GFI.
From what I see 3 parts of the two triangles are congruent. Angle EHI is congruent to Angle FGI. Angle EIH is congruent to Angle FIG. Angle HEI is congruent to Angle GFI.
You are given
Side: \(\displaystyle \bar{EH}=\bar{FG}\)
Angle: < EHI = < FGI
What does "I is the midpoint of \(\displaystyle \bar{GH}\)" say about sides \(\displaystyle \bar{HI}\space and\space\bar{GI}\)?
D
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From what I see 3 parts of the two triangles are congruent. Angle EHI is congruent to Angle FGI. Angle EIH is congruent to Angle FIG. Angle HEI is congruent to Angle GFI.
You know that corresponding sides and angles of congruent triangles are congruent.
So between the triangles EHI and EFG - which three corresponding sides are congruent?
HallsofIvy
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Are you having difficulty reading the problem? You are told that angle EHI is congruent to angle FGI. You are told that "EH is congruent to FG". You didn't mention that. As Ishuda pointed out you are told that "I is the midpoint of GH". What does that tell you about GI and IH?From what I see 3 parts of the two triangles are congruent. Angle EHI is congruent to Angle FGI. Angle EIH is congruent to Angle FIG. Angle HEI is congruent to Angle GFI.
There is NO mention in the "Given" of the other four angles you mention. Where did you get "Angle EHI is congruent to Angle FGI. Angle EIH is congruent to Angle FIG. Angle HEI is congruent to Angle GFI"?
I need help making a proof table with statements and reasons.
View attachment 4398
Let's see if we can think through a PLAN for this proof.
You're asked to prove that triangle EFI is isosceles. What would it take for us to be able to say that triangle is isosceles? By definition, a triangle is isosceles if it has at least two equal sides. So, before we can call triangle EFI an isosceles triangle, we need to find that at least two of its sides are congruent. Maybe we could show that sides EI and FI are congruent. I see that EI is a side of triangle EHI, and FI is side of triangle FGI. If those two triangles turn out to be congruent, then we could use the fact that corresponding parts of congruent figures are congruent to conclude that EI and FI are congruent, which would, in turn, allow us to say that triangle EFI is isosceles.
Look at the given information to see what it tells you about the parts of triangles EFI and FGI......do you have enough information to say those triangles are congruent?
So....here's the plan. Use the given information (and what you know because of what is given) to show that triangles EFI and FGI are congruent. Then, use the fact that corresponding parts of congruent figures are congruent to say that EI and FI are congruent. And once you have done that, you can say that triangle EFI is isosceles because of the definition of an isosceles triangle.
Perhaps this will help you to write down the statements and reasons that will complete the proof.